There are a number of "you"s here, including:
- The SDOs specifying the algorithms (IETF mostly)
- CABF adding the algorithms to the Baseline Requirements so they can be used in the WebPKI
- The HSM vendors adding support for the algorithms
- CAs adding PQ roots
- Browsers accepting them
- Sites deploying them
This is a very long supply line and the earlier players do indeed need to make progress. I'm less sure how helpful it is for individual sites to add PQ certificates right now. As long as clients will still accept non-PQ algorithms for those sites, there isn't much security benefit so most of what you are doing is getting some experience for when you really need it. There are obvious performance reasons not to actually have most of your handshakes use PQ certificates until you really have to.