Can you put a mezuzah up on someone else's home without permission?
Firstly I'm not sure why you would want to do that.
We learn in the Gemara (פסחים ד' ע"א, בבא מציעא ק"א ע"ב, עבודה זרה כ"א ע"א) and it's codified by the Rambam (Mezuza 5:11) that
שֶׁהַמְּזוּזָה חוֹבַת הַדָּר הִיא - the obligation to affix a Mezuza falls on the occupants, and not on the building.
In other words, the person living there has a Mitzva to affix the Mezuza. There's no obligation for the house to have a Mezuza; there's a Mitzva for the inhabitant to affix a Mezuza on their own house.
So you may not be achieving anything - Mitzva wise - by putting a Mezuzah up on someone else's home without permission.
Secondly, there's a problem of damaging other people's property, which is forbidden. So unless you can affix that Mezuza without damaging the doorpost (no holes, no glue, etc.) you are going to be responsible for damages.
BTW: One is also forbidden from causing damage with the intent of paying for the damage.
End result: You may do more harm than good - Mitzva wise - by putting a Mezuzah up on someone else's home without permission.