As statet here (Start docker desktop on windows without login) Docker Desktop is intended to be used as development environment and not as a server and therefore starting Docker Desktop without a logged in user is not supported. But it seems that some users have found a way to autologin with a user, autostart Docker Desktop and lock the screen afterwards.
With DockerCE on Linux it is no problem to start Docker without logging in as Docker is a service and therefore can be configured to start automatically.