When does colostrum come in?

Ana • Momma of the sweetest baby boy🌟

I will be a FTM and I read all those posts about people expressing their colostrum before baby is born. I am 34 weeks and I don't have any colostrum leaking. Some days I have bits of dry colostrum in my nipples but that's all. When is colostrum supposed to come in a decent amount for the baby? There are babies who latch right after delivery, are they actually getting colostrum at that point? Thanks!