Do you have any on-premises servers like AD or Exchange server? Is your Office 365 tenant pure online?
The original method provided is like the process introduced below: prepare a target Office 365 tenant and enough licenses. Then perform an mailboxes-migration across these two tenants. At last, add you own domain in the new tenant, and change all your users domain to your own domain; since after you migrate your users to the new domain, their domain will be changed to the new bought domain. Domain-change will be an indispensable process no matter how you perform the migration process.
Here is the official document which introduces about How to migrate mailboxes from one Microsoft 365 or Office 365 organization to another
If you'd like to perform it in other way rather than migration, Office 365 Import service could consider to be a workaround (use PST files to migrate): Overview of importing your organization's PST files
Microsoft also provides a way called "FastTrack" which may be helpful to your scenario, detailed information here: Adopt Office 365 with FastTrack
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