I'm also in the generally weak muscles camp. The OP may not have the muscles to even hold his spine in column. Sore back and sore neck are the most common issues with new riders. The solution is pretty simple: back it off. Do shorter rides and more frequent rides. Ideally, start with 30 minutes/day and try to get out most days. Don't ride hard. Take it easy. Keep track on your calendar. The next week increase your time (not mileage) by 10%. Etc. IME it's not fit. I can ride at least 50 miles on any bike that I can reach the pedals on, and I'm a talentless hack of 68 with a bad back: stenosis, thin discs, and arthritic facets.

Once some strength has been established, say being able to ride an hour in reasonable comfort, some core work might be a good idea, but all done with the back straight, no crunches, sit-ups, etc. The bike is really the most gentle back exercise there is, but even that needs a gentle progression. No one who hasn't worked out is going to do an hour of core work and not expect it to hurt.

It takes time, measured in months if not years, to get comfortable doing distance on a bike, the young and talented excepted. Be patient. It's worth it.