You can use Proton on non-Steam games. The easiest method is just to add it as a non-Steam game to your library (Library -> ADD A GAME -> Add a Non-Steam Game...). After adding the game, right-click it in your library and select "Properties...". In the properties windows, in the General tab, click the "Force the use of a specific Steam Play compatibility tool" option at the bottom. Select the most recent Proton option. Close the properties window and run your game as you would with any other Steam game.
Running Proton without Steam is a bit more of a hassle, so I don't recommend it unless you really want to avoid Steam.