Most web frameworks will retry until it can connect or give up after a specified timeout time. Basically handle it at the app layer where you have the most control.

But you still run into situations where you need to wait for docker-compose up -d to be "really" up before doing certain things (such as exec'ing into your main container to run tests or migrations).

For that I wrote a simple Bash script at https://github.com/nickjj/wait-until. IMO a problem like this can't really be solved at the Docker Compose level. But without such a script you can easily end up with failing CI tests because there's a multi-second but varied amount of delay on upping a database for the first time. That script has become a part of all of my CI / deployment pipelines.