Unfortunately, I know I'll be at a disadvantage in racing because I haven't been able to find or create a team, as all of the other people I know who are into cycling are men. I weigh 146 lbs, and my bike weighs 19 lbs. I can sustain 18 mph on my solo rides, some stats on some recent notable efforts of mine: on a -3.8 incline I averaged 36 mph for 0,4 miles, about 325 watts in-the saddle, and another sprint, at 0% incline, I averaged 480 watts in the saddle for 0,2 miles. How might I measure up in a cat 4 peloton, especially without the help of a team?
Answer: reset your expectations and give it a go.
The first race I entered, my only goal was to finish. Second time I did it, the goal was to pace better and finish with a better time than my first effort.
After that, personal improvement is really the goal, developing racecraft and strategy.
When riding in a group/bunch/peloton/paceline of cyclists, you won't believe the amount of boost received from the draught. Simply watch and learn, parrot what others do, and listen to any advise offered.
It would be good if you could do some group riding before a proper race. Look for a publicised group ride and try to join. It can be hard to ride close enough behind someone to benefit from the aero gains, and it can be unnerving to be followed closely by someone. Practice will help.
Even if you fall off the back of a group in short order, you'll experience what group riding is like. It can be addictive!
If you possibly can, ride the race route beforehand. Even some of it is better than going into it cold. Use an app like Strava etc to log a time, and expect that a bunch ride will drop your time by about 20% assuming similar weather.
Gender is relatively irrelevant in a race - different categories are all run at the same time, perhaps with a few minutes gap between the start times. IE the full length race might start at 0800 with the half-length version leaving at 0810. So there's always some mixing between classifications whether they're age, distance, gender, or whatever the race organisers chose.
As a large middle age man, I'm able to descent faster than a lighter rider, but I have to work to maintain and carry that momentum up the next climb. And then those lightweight little weeds pass me at triple my climbing speed. Knowing what kind of road is coming up, whether its a long straight descent or a 20 minute climb helps you anticipate and pre-react.
Upshot life's too short . Get out and give it a go. I've seen a guy in his 70's win his age group on a 1960s three-speed city bike.
You can't finish unless you start.
I doubt it - at the moment - but we don't know how trained you are, and proper training will work wonders. This is likely to mean finding either a club or a coach.
If your goal is to race, you really do need to find a racing club to train with. Round here there are several; all have mixed or women's fast group training rides, some also have junior sections. However powerful you are, riding in such close proximity to other riders is a very different matter.
To look at some numbers, as you imply you've been riding solo, lets look at time trials. They're simpler because they take out the aspect of peloton dynamics, and generally simplify the tactical side. As results are times, not finishing sequence, the course times are easily found online. They also have a lower barrier to entry at least where I am, and if you want to (or have to) ride solo they may be a good format to aim to compete in; distances tend to be either shorter (10 or 25 miles) or longer (100 miles, or even 12 or 24 hours) than road races, which round here seem to be 50--100 km.
I've been playing on my local TT courses recently. You don't say how long you can sustain 18 mph, but a flattish 25 miles at 18.8 mph would put me 18th out of all 20 riders (on a typical TT that uses some of the same roads). On a 10 mile course I can average 21 mph. I may actually enter a TT on that course, as I'd have a reasonable chance of not being the slowest - again I'd be very near the bottom of the table (including all adult riders). For longer TTs the slowest finishers still seem to average 21 mph - for nearly 5 hours straight.
Racing on a bicycle is HARD.
In your first race, you'll be lucky if you don't get dropped. You have no experience managing your efforts and recovery during an actual race. It's different - waaay different. One overdone effort will be enough to put you in big enough of a hole that you won't be able to hold on to the pack until you've recovered. The problem is you are going to have to make efforts to stay with the pack, but you don't have any feel for how hard you can really go without blowing yourself up, nor how many times you can do it.
There's really only one way to find out.
And you really don't know what "fast on a bicycle" means until you're trying desperately to hold the wheel of the bike in front of you lest you be gapped and get to watch the pack ride away from you. Once you get dropped from the pack, your race is almost certainly all over - if you're strong enough to catch back up to the pack after being dropped, you're strong enough that you wouldn't have been dropped in the first place.
As @Criggie noted, you won't believe the difference you get drafting in a pack. But that means that, unless you are really strong, once you're outside the pack you have no chance. If you go off the front, you will be caught. If you go off the back, you'll be dropped.
And it's really, really important to know that it's not just "I can hold X watts for 0.2 miles" - it's can you do it again 2 minutes later? Or even just 20 or 30 seconds later. Over and over and over and over.
Hopefully you have a good bit of experience in hard group rides and know how to hold your line.
In your first race, stay away from the front of the pack. You might very well feel like you can ride up there, especially early with the adrenaline of your first race flowing. Yeah, no. You'll likely feel great for a few minutes, and then you'll be hit with, "Uh oh. What have I done?!?!" as you pop and watch the pack ride off in front of you.
Also stay away from the back of the pack in races such as crits or circuit races that have sharp corners. Low-level packs will really bunch up as inexperienced riders take bad lines and brake in corners, which means riders behind them have to brake even harder - and then sprint out of the corner to not get dropped. Those sprint efforts will wear on you, and you'll eventually not be able to stay in the pack. One term used for that is "getting accordianed off the back".
Ideally, you want to be probably 5-10 riders back from the very front of the pack. Work to stay there - it's harder to ride further forward as you'll be in more wind and a lot more likely to find yourself actually on the front (if you do find yourself on the front - get off the front immediately as it takes probably 30-40% more power to ride on the front...) Further back in the pack is harder, too, as you have to deal with larger and frequent changes in speed as you respond to what the riders in front of you are doing. And all those little accelerations can eventually blow you up - and again you wind up waving "Buh-bye" to the pack.
And please don't "dive bomb" corners. Do you know how to corner? Do you know what a "late apex" means? Watch higher-level racers corner - they stay wide until late and go through the corner in a sweeping path with no sharp turns - and little if no loss of speed because they never used their brakes. "Dive bombing" a corner means thinking it's a good idea to sneak up on the inside trying to gain an advantage. All you'll do is one, go slower through the turn, and two, cause crashes. Oh, and three: everyone will hate you because you'll be "that one" - the squirrelly rider who causes crashes.
Not an answer as such but I wanted to encourage you to go for it. You probably won't win or come last, although someone has to! And inbetween you are only competing against your own expectations. I always wanted to do a triathlon but put it off for years because I wasn't fast enough (in my opinion). But last year I just look the plunge, signed myself up for a short distance and trained for six weeks. I didn't even have a bike. My aim was to finish. I didn't come last - I came in the top third and had I not done a thoroughly dismal bike leg (100 people passed me 😁) I would have been in the top quarter. I ran the fastest I ever have in my life. As others pointed out your statistics mean little on the day, tactics, strategy and the general behaviour of other competitors changes everything. And the atmosphere is addictive!
I hope you take the plunge and good luck! I am also female - it doesn't weigh much against technique at beginner level. I swam faster than three quarters of the men there 😉.
For other readers’ reference, amateur men’s road racing in the US is technically divided into 5 categories. Beginners are cat 5. Cat 1 is near professional. For women, because there are fewer women, I recall there only being 4 categories. Depending on the region and the number of people participating, races may group categories together, e.g. a 3/4 race. Regardless of gender, the OP implies they are a relative beginner in road racing.
At the lower level ranks, my impression is that the differences in strength between riders are fairly wide. Riders are still developing racecraft, which I would translate as situational awareness and decision making skills under pressure. My recollection is that good team tactics are pretty rare in men’s cat 4. Because crashes are still fairly common, the good racers are trying really hard to upgrade to cat 3. The inherent disparity in rider ability makes it harder to achieve good team tactics even if rider skill allowed it.
It’s not possible to say if the OP has “a chance“, which I assume means a chance of winning or placing in the top 10, in a cat 4 road race in the US given the information presented. I’d say that it’s unlikely that the OP will go straight from their current state to winning a cat 4 race.
However, should that matter? In traditional road racing, because of the inherent nature of the sport, we don’t care about actual finishing time, we only care about relative placing. I suspect that human cognition also plays a role - how many of you remember off the top of your head who placed 5th at the last Tour de France? How about 8th? In professional sports, we only really pay attention to the winners. In amateur road racing, we only really pay attention to high placings. The OP should definitely try it if they are interested.
However, readers should all be aware that many in the wider cycling world are a bit dissatisfied with the inherently winner take all nature of pro and amateur road racing, and that they are seeking alternative formats for amateur competition. These might be as simple as doing a metric or traditional century ride, posting the Strava Record to Reddit, and seeing how may upvotes you get. During the pandemic, this sort of solo endurance challenge has become increasingly common among many endurance sport communities. In normal times, you could enter a century of Gran Fondo, just ride as hard as you can, and take the experience. You can even see how well you place in your age and gender group. On the road, there are semi-competitive formats like audax riding, or you can take long tours.
Why do you want to race?
I've raced in plenty of races with no intention or desire to win. My goals were fitness and enjoyment. In other races, my goal was to win and I trained accordingly.
Without us knowing the stats of the competition, and your degree of training, it is hard to know how good your chances are of winning.
I encourage you to think about why you want to race. If racing can fulfill your goals, go for it!