Keyboard/Joystick Inputs Do Not Work until Mouse Clicked

I'm finding that keyboard and joystick inputs to our game do not work (don't register via any scripts) until our full-screen game is clicked on once with the mouse.

This only applies to the full-screen build of the game. It works fine in the Editor.

Does anyone have any idea what the problem might be here? We'd really like our game to be immediately playable via a gamepad or keyboard, as there aren't any mouse-driven menus on startup.

Here are the build settings we are working with: