You can just have a gmail account you don't use, and in fact even if you have your own domain, if you're willing to pay for Google separately, you can have a Google Workspace account for your custom domain and your e-mail for that domain at Fastmail and just not point any MX records at Google. It works fine - it's what I do as an artifact of having used them for e-mail and moved but not having bothered to untangle my other stuff (yet; but it's been years).
The only thing that's a bit of a hassle is the calendar. It also mostly works, since you can add your Fastmail calendar to Google Calendar, but Google is slow to sync.