Apple TV setup to theatre system

Assuming the projector has HDMI inputs you can connect the Apple TV directly to it. If you are using a Home Theater Receiver, connect the Apple TV to an HDMI input on the HT Receiver and the Receiver should output the video to your projector and the sound through your speaker system. Your setup seems pretty common but we don't know what inputs your project has or if you are routing through a HT receiver.

You can connect it more less to anything with an HDMI input. Using it with out a TV screen may be a challenge

🤷🏼‍♂️ Is the set top capable of through put? Many are not. Try it.

Connect the Apple TV directly into the set top box with an HDMI cable (you will need enough 'input' slots on your set top box.