>> Is this a problem that isn't present in Bitcoin? How can a brand new Bitcoin user securely join the network for the first time?
> It worries me that you can't answer this and you're working on a cryptocurrency.
I'm not asking because I don't know the answer. (I know the answer.) I'm asking because your answer will help me clarify the answer for you using the framework and terminology that you're comfortable with. And in this space, each term means different things in different contexts. :)
It's not trivial for a traitor to pretend to be all of the generals. Say there are validators A, B, C, D, and they have equal voting power. Given this configuration, it's impossible for A to be the proposer for 2 blocks in a row unless some of the other validators were absent. It's not just deterministic -- it's round-robin.