I'm looking for ways to replicate a Postgres database on an on-prem server to AWS RDS. I normally connect to the database via AWS SSM Session Manager (because the ip address keeps changing).

Ideally, I want to use an AWS managed service to handle the replication. I looked at AWS DMS, but I don't see any way to setup a connection through Session Manager and instead would have to specify an ip address.

Is there a way to setup a DMS endpoint through Session Manager or alternatively, is there another managed service I can use for this scenario?