Here are a few ideas for a Rube Goldberg machine that closes a fridge door:
A marble rolls down a ramp and hits a small lever.
The lever activates a toy car that rolls down a track and hits a domino.
The domino falls and triggers a chain reaction that results in a weight falling onto a lever.
The lever pulls a string that is attached to a door handle.
The door handle turns and the fridge door closes.