The "core" will get stronger with more time on the bike.

However, I think you're right, setting the seat back a little may help relieve some of the hand pressure. It is usually an easy adjustment with a set of Allen wrenches. Each seatpost is a little different, but essentially figure out how to unclamp the rails, and push the seat back, then retighten.

I believe that moving the seat forward requires a higher post, and back a lower post, so you may also have to adjust the seat post a touch.

If you're new with the adjustments, then it wouldn't hurt to take some photos and careful measurements of your current configuration so that you can always go back to where it was if you wish.