Azure AD before Exchange migration?

If you want directory sync then rule out cutover migration. You can't do the dir sync before the migration, and it's challenging to retrofit it after the migration.

Choose a migration method that uses dir sync up front. That means either Staged or Hybrid. Staged is a fairly blunt instrument and is still a cumbersome user experience and support burden, but at least you can manage it in smaller groups than an all-in-one-big-bang-cutover migration.

Hybrid is the best balance of administrative control and user experience. Since you want directory sync anyway you will need an Exchange server on-prem for ongoing management of the Exchange attributes in AD. 2007 is end of life, so you will need either 2010 or 2013 for that purpose. You can get a free "hybrid license" to fulfill that role.