Unless a frame is grossly mis-sized, it's difficult to tell from a single photo on the internet.
Bike stores are supposed to size you. That is, someone will sit with you and perform some basic adjustments. They'll set the saddle at roughly the correct height and fore-aft position. From there, they should look at you on the bike.
In particular, we would want to see you with your hands on the brake hoods, not on the bar tops where they are in the photo. If your saddle is in the correct position, your arms should be slightly bent in the hoods. If you instinctively prefer the tops of the handlebars (your current position), that can indicate that the reach is too long. Now, the distance from you to the brake hoods can be changed by fitting a longer or shorter stem. Sometimes, bike stores are willing to swap the stock stem with something they have on hand if you know what length stem you need. They can also raise the bars vertically if needed. But if you have a short stem and you need the bars closer, that would be bad.
Paying extra for a bike fit is an option that people should consider. The retail assistants working in bike shops will size people using an algorithm provided by the bike manufacturer plus some basic knowledge. Bike fitters have more advanced knowledge. Coincidentally, Cycling Weekly recently published an article featuring a new cyclist who went for a bike fit before buying.
Of course, most people don't do this, and most of us buy a bike and then modify our fit after the fact using our own perceptions and information we hear from others - some of which might be wrong in general or wrong for you.
In any case, at minimum, I'd approach the store in person and ask to be sized to the bike. Trek does accept returns of bikes (and other things) within 30 days in like new condition, so that can be your last resort. If you take a test ride and you feel like you are stretching too far forward, that's not good - to some extent your body can adapt to a more aggressive position, but you shouldn't be doing that with your very first bike unless you're very athletic and you know you want to get into racing. Visually, I concur your saddle is too high, and I think most experienced riders would agree. Move it to the correct height and that should slightly reduce the reach to the handlebars. Do that and then see if the handlebars are at the right distance.
