Add your domain USA.Compaby.com as an UPN suffix and update your users to them. Best idea is to match it with your e-mail domain. You use AD Domains and Trusts for that.
Then sync those accounts with Azure AD Connect. Start with very few, so you see the results. In Azure AD Connect do OU filtering. And just chose a single OU as a start. Use standard PWD hast synchronization with SSO.
Use a Custom installation of Azure AD Connect
https://learn.microsoft.com/en-us/azure/active-directory/hybrid/how-to-connect-install-custom
If you start with one or two users in your OU, this operation should be completely non-destructive.
You might want to start with a test environment and document all steps with SnagIt. That's what I usually do. But if you are careful and follow the instructions, this should work the very first time.
Later you can add other users to the OU. If you remove some, they will be deleted from Azure AD. You can add other OUs as well. My usual setup is OU My Company and a lot of sub-OUs. My Company is then the only OU synced.