The sooner you start finishing, the easier and neater the job will be.
Sometimes I'll put a
complete first coat of finish on a piece before it's assembled, but in the case of these cabinet doors, which were cut to finished size and sanded after the glue-up, that would have been a waste of time. On the other hand, the panels for these doors, seen in this previous post, were not just prefinished, but finished differently than the door frames, so I could really highlight the 3-D effect of the burl. Getting stain and then topcoat onto the inside edges of the doors, without messing up the finish on the panels, would have been like manic depression. (You'll remember Jimi Hendrix referred to manic depression as "a frustrating mess.")
So before I assembled the doors, I stained their inside edges, then sealed the stain with shellac, then put on a coat of water-based acrylic - - - the same finish as the rest of the frames, just sooner.
This has the additional benefit of making glue squeezeout trivially easy to clean up.
The sooner you start your finish, the sooner you'll finish. Just be mindful about it. There'll be more on this door project coming up.
PS) If you're thinking that going through all the finishing steps separately for this tiny detail adds unnecessary time, I'm betting you've never tried to clean glue squeezeout off of bare wood in door corners before, and then found out when you stained that you didn't get 100% of the glue. Believe me, if you're staining, this saves time and gives you a better result.