Generally what I have done in the past is use an update mechanism.
Most platforms allow you to do updates post-purchase.
The update is generally not a full download of the game.
Be warned though, some target platforms charge for updates. Others only allow a small number of updates for free, then they start charging.
You will have to do your research.
However there are some tricks you could think about.
You could modify Monogame to get the built content files from a URL, you could use your own file formats and bypass the content manager entirely, if all you are interested in are desktop machines, you could just have a public directory on the machine with all your own files in it.
In short, you need to come up with a plan and code it.