It took a lot of time, honestly. But I really wanted to extract myself from Google and cleanup my email, so I did everything manually, sending emails to friends and family from the new account, getting rid of any old emails I absolutely did not need, and forwarding any archival stuff I could not let go of to Fastmail and/or exporting emails and docs to my PC.

That said, Fastmail does have an import function, but I did not use it when I migrated: https://www.fastmail.com/help/receive/migratemail.html

edit: word choice