OP- you need to take the lead if you want it done earlier. Your daycare has told you they won't do it before a certain age. And personal meetings around potty training? Over the top.

It starts at home. Don't lie, the provider will know.

We trained our second at home and didn't send him to daycare in underwear until he wasn't having daytime accidents at all. It didn't cause regression to go back in pull-ups at day care. I think it's ok to do this at home.