You can use hg-git[0] to push to Git from a Mercurial repository. Then it's basically just like working with another Git repository. It does mean that you need some way of mirroring the two. I've never tried it, but it looks like you can use git-hg[1] to use a Mercurial repository like a regular Git remote.

[0] https://hg-git.github.io/ [1] https://github.com/cosmin/git-hg