Can I activate PITR after the DB has been used My Postgres-Server is running for quite a while and contains probably 4-5 GB of data.

Backups are done using dumps, and this works ok. Though not most efficient, it just works.

Due to future growth I like to activate PITR backups (like RMAN in Oracle).

Is that possible and/or recommended? Or would it be better for me to recreate the DB with the correct settings upfront?
No need to recreate the database.  Set up archive_mode and archive_command, restart the server, create a base backup, and there you go.  (Details vary depending on version.)

It is quite common to "upgrade" from pg_dump to PITR backups as the database grows.