It's fairly rare for microwave range hoods to be vented outside in newer homes unless specifically requested by the initial owner (at least in my part of the world, where any exhaust vent wastes expensive heated interior air). They're set up from the factory to be recirculatory, running air through charcoal filters and/or wire mesh grease traps, then out the front louvre. By reversing the fan unit housing they can be configured to vent to the exterior.
Your microwave is probably supported by two screws through the floor of the cabinet above. These are very long and can be loosened up to an inch or more without the microwave coming unattached. They typically fit a #3 Phillips or large flat-blade driver. (Using a #2 driver can result in screw damage.)
With an assistant, loosen one of the screws an inch. Verify that it hasn't come completely out of the threaded socket it runs into. Now, while your assistant supports the front of the microwave, loosen the second screw. Lower the front of the microwave and have a look over the top, under the cabinet. The unit will be supported at the lower rear by a bracket flange.
Your microwave's vent either exhausts upward or rearward, but from right at the top rear of the unit. You'll be able to see whether there's a duct opening at that location. If necessary, completely remove the screws to lower the unit further.
Snug the screws up when you're finished. They don't need to be overly tight.