How do you get better at sit starts when bouldering?
Climbing on the moon board really helped with my sit starts, something that I was fairly bad at. I just couldn't get myself off the ground.
After dedicating a few months to climbing on the moon board, besides getting stronger in my core and grip strength, sit starts became much easier for me, since, at least in my gym, the moon board sit starts are much harder than the regular routes sit starts.
Besides that, I believe that supplementing climbing with weight training can help a lot with it.
What really helped me get better at sit starts was climbing on a moon board, and either finding boulders that have sit starts, or building new boulders with sit starts.
I was pretty bad at sit starts since they are very compressed for me, something I am fairly weak at. But after climbing for about a month almost only on the moon board, I really saw the improvement, and it was very noticeable.
I still work quite often on the moon board, and I can really see the difference from before and after. I try to do the most disgusting sit starts possible on the moon board, and I can do all of the sit starts on the regular route setting walls.
The moon board in my gym is a 30 degree angle I believe. If you don't have a moon board, I think you can probably do the same on any other system board.