Is it possible to add a DB to an Always On AG and setup replicas at different time? I have a 3-node SQL Server Always On availability group. 2 nodes are on the same LAN, and the third one is on a remote site with high latency.

I will add a huge DB (10TB) to the AG, so I would like to be able to just get it added to 2 replicas on the LAN in a first stage, and some days later, to get it added on the 3rd (remote) replica after manually copying it on-site. 

Is this a supported scenario?
If so...What would be the recommended approach?

Adding the database to all nodes at the same time is not an option unfortunately.
I would recommend you either restore/attach the database to the primary node on the SQL server. From there you could add it to the AG but not have it replicate. Ultimately, to get it on the 3rd(remote) node - you'd likely have to break the AG and re-add the database (if you're allowed the downtime) after it's already copied to the remote node. This would allow it to sync up.

So this approach would mean you'd have 3 stages:


Stage 1: 10TB Database on Primary Node restored/attached - not in AG
Stage 2: 10TB Database added to AG. Remove remote node from AG.
Stage 3: Copy 10TB on remote node. Rebuild AG to include remote node. Allow AG to sync and catch up with data.


If this isn't clear let me know more so I can help you (such as OS/SQL version).