I packed mine a month ago. I'm 33 weeks and 3 days. I just add to the bag as I go. I've had so many preterm scares that I'm glad I packed it.
You can pack whenever you want :) I'm gonna pack mines after my baby shower so I can wash everything & make sure I have everything. I'm 33 weeks & 6 days :)
I am having a homebirth, but I packed an emergency hospital "just in case" bag at 27 weeks (I'm the kinda person who has emergency kits for everything though).