One possibility is to have the power to the raspberry turned on at the same time as the projector. It would then lower the screen on boot. Your problem then moves to the end of the film, when you need to signal it to retract the screen and shutdown cleanly.
Controlling a relay is trivial - you will find plenty of examples online.
Using a small relay that stands in place of a button to signal up or down to the screen motor is obviously a lot safer than trying to control mains voltage. If you really need to switch mains voltage and do not have absolute confidence that you know what you are doing I would suggest something like an Energenie (https://shop.pimoroni.com/products/pi-m ... gJtYPD_BwE
) instead of trying to use a relay.