My recommendation (assuming you have a normal @gmail addy and not a custom domain like I had) would be to use email forwarding. So you can leave your Gmail as is, but set it up (in the settings) to automatically forward all your email to your new protonmail address. Then you can gradually change the important contacts/sites to your new email at your leisure.

I do highly recommend buying a domain and setting up your own email address though, it gives you a lot more portability going forward. You can actually do a lot with your own domain, and it helps you maintain trust better.

Anyway, enough preaching lol, protonmail also maintains a guide to help people switch: https://proton.me/easyswitch