Sounds like your challenge is more about integrating the containers in a useful pipeline to get ephemera (preview) environments. Like deploy a new env for each PR and update each env when it's branch gets a new commit.

An easy way to get ephemeral envs starting from your docker-compose definition is Bunnyshell.com. It uses Kubernetes behind the scenes, but it's all pretty much abstracted away from the user. There is a free so you can experiment.

Disclosure: I'm part of the Bunnyshell team.