Is it possible to mount a countertop microwave under a cabinet?
There are 2 issues here:

1) Top clearance. Countertop ovens usually have vents on top and the manual states the minimum clearances - from top, back and sides. Countertops generally need space around them.

2) The physical mount. You're showing a floating shelf bracket, but there is no shelf. Countertop appliances have wide-spaced legs and they are designed to stand on those legs to be stable. If you plan to put it on the bare bracket, that's not a good idea. First, it won't be stable enough and could tip to the side and slide away. Second, "the belly" may be just a heatshield and only the legs are structurally strong enough to hold the weight of the oven. Third, bottoms of countertops are usually exceptionally ugly and you're exposing it to anyone who bends over.

I believe you should just build a dedicated shelf for the oven. Take the minimum distances into account. Make it at least as big as the legs. Add small side fences or mount rings into which the legs will sit to prevent the oven from being easily knocked off it.