I recently found out about Podman (https://podman.io). Having a way to use Linux fork processes instead of a Daemon and not having to run using root just got my attention.
Yes, that is doable now, check podman-compose, this is one way of doing it, another way is to convert the docker-compose yaml file to a kubernetes deployment using Kompose. there is a blog post from Jérôme Petazzoni @jpetazzo: from docker-compose to kubernetes deployment