I started contributing to a lot of smaller projects, both paid/unpaid, my own/others'. At the next job change I mentioned that I need permission to finish a project and HR offered me part-time with a lot of flexibility. That said BigCorps usually are more open to part-time or might even have fixed programs so not any negotiating might be necessary. But generally I'd ask when it's clear they really want to hire you.

Once you've had part-time experience it's easier to continue at the next place. By the way, people might try to nudge you into fulltime once you're there so quite some discipline is needed to keep a fixed schedule.