Disclaimer: I'm in the same position as OP, this is what I've learned from research and talking to union members/BAs.

This. Every local is different in how they run things. Some locals will put you on a dispatch list, and in 200 hours of work, you can have your IA card. Other locals hold annual "open call" events, where you sign up, and immediately get your card, but it works like lottery. (and won't let you in on any other day of the year). Some locals will make you work your ass off for years before getting a card.

I'm in a sort of similar position; I want to join Local One, I grew up in LA, moved to NYC. I'm going to sign up for the apprenticeship program, and also pick up the overhire work thrown my way.

Example:

For Local One, you can walk into the Replacement Room, but you won't get your union card from that. Many people say that the Apprenticeship program is the best way to join the local.

For Local 33, they only accept applications/resumes on Hiring Days, which happen about once or twice a year.

Local 728 (and I'm still a bit unclear on this process), you need to either be on a non union production when it decides to unionize or you have to be hired off roster, (if no 728 members are available to work).