As the sibling comment mentioned, this is a solved problem. MySQL and MariaDB take a very brief lock on the table at the very end of index creation that you will not notice, I promise. Postgres does the same if you use the CONCURRENTLY option for index builds.

If for some reason you do need to migrate data to a new table, triggers.

If somehow these still don’t solve your problem, ProxySQL or the equivalent (you are running some kind of connection pooler, right?) can rewrite queries on the fly to do whatever you want.