Also host docker image on DockerHub or include natively within GitLab CI Runner

We would like to utilize this docker image, however, due to firewall restrictions we are unable to access it via the quay.io domain.

Can the docker images also be pushed to GitLab's DockerHub account so that they are publicly available from there?

Alternatively could it be possible that this feature is bundled directly within the GitLab CI runner so that it is natively checking that it will not fill up disk space due to the cached images / containers that are left behind over time.