How to patch a hole behind a microwave?

Thanks for writing in!

First and foremost, ensure there’s definitely a stud the microwave is going to be mounted into (the image looks like insulation or wood), no joint compound or drywall will have the strength to hold a microwave. Check the microwave manufacturer instructions for any mounting plates that might need to be installed.

Since this hole is going to be covered by the microwave, it’s more cosmetic and a barrier for moisture/rodents/insects. If I had to repair this before installing the microwave, I would use Easy Sand 5 or Easy Sand 20.

The reason I’d go with this is because it’s a compound that hardens within either 5 or 20 minutes. Mix some of the powder with water to get a very thick pancake consistency, and stuff it in the hole with a taping knife, then smooth the outside. Since it’s being covered it doesn’t need to look perfect. Only the 5 minute comes in a small bag but it would definitely be my choice.