I just finished my first project and found that painting the cabinets was very time consuming - especially so since I used oil base paint which takes forever to dry.
For my next project, I'm considering painting all of my pieces first once cut.
I think it depends somewhat on how you plan to assemble things. I'm not sure if wood glue will adhere to paint (maybe it does,but I've never tried).
If you are going to glue things you could always cover the parts that will be glued or avoid painting them and just paint the pieces and then assemble when dry.
If you get any scratches or have spots where you want to fill in, you can always do some touch-up paint after.
You could probably try painting first and see how it works for you and which method you prefer better.
I admit that I've had trouble getting in to spaces to paint when something was already assembled.
Spoiler: I know nothing! But I did finish and assemble an unfinished bookcase and the recommendation from the company was that one ought to stain the pieces before assembly. From actual experience in other projects I can say that stain will not adhere well to glue. So that experience might support the idea of paint first, glue second (presuming there's some similarity between paint and stain behavior).