Your existing emails will need to be transferred if you want them available in FastMail. You can either do this manually using an IMAP client (set up with both Gmail and FastMail) or use FastMail's IMAP migration tool. Whichever way you choose to do it, you may well end up needing to do some deduplication (which FastMail partially automates) because of the somewhat eccentric nature of Gmail's IMAP support. It is a pain, but a one time process.
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