[Mikendebbie]

I have done something like this on a former SOB. See the screen shot below.
If it was me I would try to mount plywood on both sides of that wall then mount the tv to the outer plywood. The wall is most likely hollow with maybe 1x2 wood stud frame around the perimeter. You can do some investigating using some small finish nails to poke around and try to find studs. Maybe you do it down low on the wall where your test holes won’t show up. You will have to pull the fridge out and verify that there is enough room to get a backer plate plywood screwed to 1x2 perimeter frame and still fit the fridge back in place. The TV mount will go on the outside plywood. I think if you can anchor plywood firmly on both ends the plywood will span and support the TV. The bolts for the tv mount should go thru both plywood backer plates. In addition to screwing the plywood to the studs I would apply liquid nails and glue both PCs in place. The glue and the screws should offer enough support. The key is getting the backer plate inside where the fridge goes. I would be hesitant to mount the tv to the exterior plywood only without the inside backer plate. Thru bolting both pieces will help! All of this is speculation on my part but I would be shocked if they used aluminum to frame that fridge enclosure.