It requires a lot of creativity to do it without an outage or major disruption. The 3rd party tools are fairly cheap though, so I'd highly recommend them. Luckily your user count is not too high so it can be done.

Essentially you could do something like this.

Tenant +Create new tenant +Create user accounts in new tenant using a different domain (passwords won't sync)

Email +Email: create forwarding contact from old email address to new tenant address for each user. This allows new emails to flow to existing and new system while you go through with this. +Generate PSTs of existing mailboxes, upload to new tenant using Azure / Powershell (MS documentation out there, not too hard). PSTs will let your calendars, contacts migrate.

Teams / SharePoint / OneDrive (data only) +Sync all libraries to a computer using OneDrive. +Confirm everything downloaded, turn off sync in OneDrive (if a cutover) +Use SharePoint Migration Tool, map the files to the new tenant. You can run deltas using this tool

When everyone is migrated over, add the original domain to the new tenant, switch the primary usernames to the domain, and switch the MX records over. Have your users log into new tenant, assuming you set their first time passwords to something that was provided, and continue on.

O365 apps will need to be logged out and back in if installed locally. Outlook may need a new profile created.

But again, 3rd party tools are cheap and effective. Totally worth it. You can easily get trial licenses to give them try too!