Great question, it's not timestamps but attestations (signed validator votes for pairs of checkpoint blocks) that determines the canonical chain head. This fork choice rule, known as LMD-GHOST, is different from PoW which has a "greatest difficulty" rule for determining the canonical chain.

There is some element of bootstrapping who the original validator set was, known as "weak subjectivity". There's a great post from Vitalik exploring this further at https://blog.ethereum.org/2014/11/25/proof-stake-learned-lov...