What is the fastest way to make a copy of a 5TB SQL Server DB on the same server without having to fully reinitialize the DB to add it to the AG
&quot;I could use a tranlog backup, and then roll it to 12:01am&quot;
Do that.  You can restore the last full backup, then apply log backups with NORECOVERY in the days or hours before the first of the month, then apply the last log backup with STOPAT and RECOVERY or STANDBY.
Or you could create a Database Snapshot at midnight on the first of the month.  That would avoid copying all 5TB at the beginning, and the snapshot will only store pages that change over the course of the month.