It's relatively easy to setup the Xbox One Wireless Controller to control all aspects of this game, but it requires some familiarity with using or creating controller configurations with Steam, so I created a config for you so that you don't need to bother.

Make sure your controller is connected. Open Steam Big Picture mode and navigate to the game. Click the button with the Controller icon, and click "Enable Steam Input". Now, repeatedly click the "Back" button until a panel opens on the left. Click the "Power" button and then click "Exit Steam Big Picture Mode" to return to the normal Steam layout. Now, go to the next step of the guide.

Alternatively, if you prefer to use Big Picture mode, you can instead click the bar under "Current Button Layout" and then click "Community Layouts" or the Search icon at the top of the screen. Look or search for "Master Zoen's Split/Second Gamepad". Click it, then click "Apply Layout" in the bottom right corner of the screen. Skip the next step of the guide.

Copy and paste the following link into a web browser and then click "Apply Configuration" to download the controller configuration.

steam://controllerconfig/297860/1749568916

This will make the dpad function as the "arrow" keys, the View button will function as "Esc", the Menu button as "Enter", the X button as "Tab", and the Right Bumper as "Space".

Start the game and use the dpad to navigate to "Controls" and select it with the Menu button. Press right on the dpad until you get to "Joypad 0". You'll notice that there is a dash mark in front of "Vehicle Throttle". This is how you know what action you are setting.

Press the Menu button and then press the Right Trigger.
Now press dpad down, then menu, then Left Trigger.
Now press dpad down, then menu, then tilt Left Stick to the left.
Now press dpad down, then menu, then tilt Left Stick to the right.
Now press dpad down, then menu, then A.
Now press dpad down, then menu, then B.
Now press dpad down, then menu, then tilt Right Stick up.
Now press dpad down, then menu, then tilt right stick down.
Now press dpad down, then menu, then tilt right stick to the left.
Now press dpad down, then menu, then tilt right stick to the right.
Now press dpad down, then menu, then Y.
Now press dpad down, then menu, then Left Bumper.

When finished the settings should look as follows:

Now, press the View button to exit the "Controls" menu.

Congratulations! You've now configured the game to use your Xbox One Wireless controller and won't need to use the keyboard.

I hope this helps you enjoy the game!

Credit goes to wearecity for informing me how to select the Controller in game.