Without cached data from a previous visit, 1-RTT mode works even if you've never vistited the site before (https://blog.cloudflare.com/rfc-8446-aka-tls-1-3/#1-rtt-mode). It can fall back to 2-RTT if something funky happens, but that shouldn't happen in most cases.

0-RTT works after the first handshake, but enabling it allows for some forms of replay attacks so that may not be something you want to use for anything hosting an API unless you've designed your API around it.