I have had a numbing sensation in my thumbs. I take it it is caused by the pressure of holding the handlebars while riding. The bike is a Schwinn Signature M3030 - SR SUNTOUR mountain bike.
Could be the position of yours hands, which you can adjust yourself, but is more likely a combination of the over all bike fit. Things such as seat position, handlebar height and a variety of other things all play a part in how much pressure your hands exert onto the handlebars. Riding a bike that is too large can have your body leaning to much on the bars and exerting too much force on your hands and wrists.
Depending on what grip you currently use you might try changing them to something a bit softer such as some of the silicone variety, ESI or similar for example. Sometime gel padded gloves can help but I would venture to guess that it is a bit more complex and probably related to the over all fit of the bike.
If you ride often numbness is definitely something you should take seriously and if it is worth the money and you do ride often, you may think about having a proper fit done at a shop or at very least take your bike in and explain the problem and get their opinion.
Also, make sure you are not gripping the bike too hard, sounds silly but it is possible, your grip should be firm but semi relaxed, not holding on for dear life sort of grip.
Lastly, the angle of your wrists can also be a factor, depending on what type of shifters/brake lever you have you might try adjusting them downward or upward to try and find a more comfortable and natural position.
I have grips with flats on them to spread the load, rather than plain cylindrical ones.
When I changed bikes to have front disc (no suspension), the forks are now straight and rigid, and there is far more shock (speed bumps, potholes) and vibration that the previous bikes.
So I also got these flexi handlebars . As you can see they are also not straight, and I find that also helps with a better wrist position than straight mtb bars. I am pretty happy with them.
I have noticed riding my mates bike with suspension, that while the shocks (hitting big lumps) are reduced, the vibration comes through the front shocks unchanged.
A numbing sensation in the thumb is probably because you're compressing a nerve in the base of the thumb (the Abductor pollicis brevis muscle, the big squishy one).
Personally I get the opposite - a numbing of the little and ring fingers, which has the same cause but on a different muscle.
Its also possible to numb digits by restricting blood flow, and can be exacerbated by the cold and not moving the muscles much.
Move/reposition your hands about the bars a bit more. Road bikes with drop bars have a lot more positions, as do trekking bars. You can also fit barends or barmids for another place to hold onto, albeit with no brake levers.
Move/flex your hands more. In city riding, signalling should get your hands off the bars and give some muscle movement. Avoid staying locked in one position for longer periods. You can put one hand in turn behind your backside and give it a flex for 10-15 seconds every 15-20 minutes and that helps. Then do the other side, and each foot/ankle/leg in turn too.
Wear padded cycling gloves. They don't need a lot of padding, 5~6 mm would be very thick and 2~4mm would be normal. Thin single-layer gloves are more for sun protection or aero, so skip them. You can wear two layers of gloves too. I've seen someone tape a couple of cotton balls to their palm then fit a glove, to help put pressure elsewhere than their nerve.
Be warmer - kinda related to gloves but not quite. If your extremities are cold, they work slower and sensation is reduced so you can't feel the numbness growing.
As a tall person I have problems finding long-sleeves that reach, and they're rarely affordable. So my riding clothes for winter always include two old socks with the toes cut off, to cover over my riding top cuffs and then to be tucked inside my riding gloves.
(I even wear them in summer to help with sunburn on longer or midday rides.)
Thicken up your bartape. There are foam bartape offerings that add a good amount of thickness. This works better on drop bars, but I've successfully used bartape on flat bars in the past. You can put cheap thick foam tape on as a first layer under your nice outer tape at the main resting points, but the outer won't go as far because its now further around.
You can simply buy new grips if you prefer that kind of hand grip. There are round and wing-ish shaped styles, so try them out.
Lessen the weight on your hands. Sit up a little more, press harder on the forward pedal to take some weight off your hands. Try sliding your backside slightly further forward to achieve a similar effect, or lower your saddle a bit or raise the handlebars.
If these suggestions help the hands at the cost of something else, then your bike fit is suboptimal and needs a tweak.
Larger and/or lower-pressure front tyre. This will help soak up more of the road vibration, at the cost of less aero and probably more rolling resistance.
Tweak your suspension, if you have it. Few road bikes have suspension, its mostly the domain of MTBs. But some bikes have a fork shock or a headshock, with an elastomer or spring or oil/air somewhere. You might be able to replace a part if its worn, or increase the squishiness of the insert with a new one. Air and oil suspension generally has a valve somewhere.
Your fork is:
SR Suntour M3030 27.5" Coil Spring, 75mm travel Alloy crown and lowers I'm not a suspension person and can't comment if there are any tweaks you can do with that, like adjustments. Hopefully another SE user can comment on that part.
You have the classic symptoms of carpal tunnel syndrome.
Numbness on the thumb side of the hand is carpal tunnel syndrome. Numbness on the little finger side is called ulnar tunnel syndrome or Guyon's canal syndrome.
A significant factor is the position of the wrist whilst riding. Wrist extension, raising the back of the hand, whilst putting weight on the hand is problematic.
Drop handlebars as opposed to flat handlebars lead to a much better riding position for these hand conditions. Particularly riding on the hoods which gives a straight wrist.