When people think of ‘strengthening the back’, they often think of doing sit ups.
This common myth is simply not true! And harmful for your back.
A traditional sit up places enormous amounts of stress on the discs, joints, and surrounding tissues and should be avoided at all costs (simply read the research e.g. Low Back Disorders - Stuart McGill). Each time you do a sit up, it places as much force as American/Canadian Work Health and Safety Taskforce says to avoid at all costs. Each sit up is pushing you right up to the unsafe limit!
With any back pain, first priority is to normalize the biomechanics!! (make sure the joints are working properly and in the correct order - as other have mentioned here “control issues”). In my opinion, you cannot start strengthening without fixing this mechanics first; it simply makes no sense. And to do that, chiropractor is first choice.
THEN, and only then, you can start strengthening/rehab on the lower back - which physiotherapy would be good. Inline with the other professionals opinions about exercise, back endurance exercises for transverse abdominus, gluteals, etc are a good start (such as dead bug, back bridge, bird dog, etc). And a final note, everyone is individual so a tailored treatment plan is needed.
Hope that helps clear up some of the myth on sit ups/back strengthening!