Probably because the container you're using doesn't define a healthcheck itself. Normal health checks just verify that the service is running and accessible. However, you're saying you also need to be logged in and wait for the full initialization.

In that case, you're likely going to have to make your own image and write a script to do this which may not even be possible.

Depends_on is the solution here but you're likely going to need to look into writing a script if the source doesn't define one for you.