Cloud Migration (Migrating physical infrastructure to the cloud)

So just a single server domain controller, is there file shares on it as well or is it just Active Directory? An approach you can connect your Azure virtual network to your onpremise network (I have a linked in post that provides info on that https://www.linkedin.com/posts/jeremyjwallace_connect-your-network-to-azure-in-4-easy-steps-activity-7104894065686548480--snG?utm_source=share&utm_medium=member_desktop)
and then you can spin up an azure virtual machine and join it to your existing domain and promote it to a domain controller. Then all your users and computers and dns in active directory will be replicated to that new azure based domain controller. If you have an file shares on the server you can move those to azure file shares instead of having them on the domain controller. I have a video on how to use Azure File Sync to migrate file share files to Azure Files (https://www.linkedin.com/posts/jeremyjwallace_using-azure-file-sync-to-migrate-from-windows-activity-7128772467141054466-Ehax?utm_source=share&utm_medium=member_desktop).
So that would be my initial recommended approach but if you have a lot of other stuff on there then yes I'd probably recommend using Azure Migrate first and foremost as that's going to give you a good analysis of your current setup and help you size your VM correctly in azure and handle the replication.