Does the hole go all the way through the floor underlayment material and open to the outside underneath? From your description I'd say no, that there is a 'pocket' that could hold some type of filler material.
The photo seems to show a 'flap' of linoleum. If so, if that 'flap' is pulled up would it come close to matching the edges of the hole?
I've never worked on anything like problem that you have. However, I'm thinking that if you can carefully pull the flap up and then fill the hole to level, you could then glue the flap back down to be level with the rest of the floor. I haven't a clue how you would hide the edges of the flap. It may not look like new, but maybe it would be passable.
Sherm & Terry w/rescues Steve (std Poodle) & Eydie (min Schnauzer)
2015 Jay Flight 27RLS (Camped: 102 nights 2015, 90 nights 2016)
2006 Ford F350 6.0 PSD, Lariat, 4WD, CC, LB, SRW, auto., Camper pkg.