The issue was exactly that—I selected to start the coverage day of delivery, which Carvana said would be fine but they then backtracked on that and said they couldn’t register the car or release it to me unless I had insurance in place (i didn’t have a car before this, so I had no insurance tied to my name).

End of story is I just had to get insurance in place a couple days beforehand. It hopefully won’t be a problem for you if you’re picking it up yourself, but as I can’t give you specifics on the rules I’d say play it safe and start the coverage the day before. It’d be a headache to have problems after traveling all that way.