Goat Simulator 3 doesn’t natively support controllers on PC for some reason. This is despite the fact that the first title did, and the threequel game is available on consoles.
Since the game is also exclusive on Epic Games Store which, unlike Steam, does not support controller input as a workaround, there isn’t a normal way to use a controller for this game.
What’s even more strange is Coffee Stain North’s apparent workaround for this issue. On the Discord server for the game (via Neogaf), they have set up a bot telling users how they may be able to use a controller with their recently launched title.
The surprising answer is to use Steam. Specifically, they state to add the EGS client itself to Steam and launch it from the Steam launcher. From there one would be able to use Steam input with their desired controller of choice to be able to play Goat Simulator 3 with a controller.
They also have a second solution which involves using third party software for PS4/PS5, or a specific guide for Xbox controllers. However the fact that a game which is exclusive to EGS requires using Steam for controller support is ironic.
Goat Simulator 3 is out now for Windows PC (via the Epic Games Store), Xbox Series X|S, and PlayStation 5.