The more RAM the better. I would not start it with less then 8 GB.
If you want to run your own search server too, I would suggest at least 16 GB RAM.
(The mentioned 4 GB RAM and 2 Cores from the documentation are the technical minimum, don’t even try it.)
You can open a second terminal window and enter this command line:
sudo docker-compose exec musicbrainz /usr/bin/tail -f slave.log
Then you can see the processing of every single replication packet (produced every full hour).
BUT:
Don’t start to replicate from 2018-08-14, this will take forever.
Download and import a so called “Full Data Dump” - only some days old. Replicate then the missing packets until now.