Move 401k to new employers?

Currently have a 401k with Schwab, which is what my previous employer used. Working with a new company now and they use Fidelity.

My question is: should I transfer the balance from Schwab to Fidelity immediately (I just started with new company) or wait a little?

Is there a better option to have an independent provider that I don’t have to make these moves when I switch jobs?