To put it in perspective, the escape hatch is probably about 20 inches square and the exhaust fan, if it's a standard RV type unit, probably is designed to fit a hole 14 inches square. That makes a 3 inch gap all the way around if the fan is centered in the larger hole.
If the inner hole is formed so that it has a lip rather than just a thin edge, a much thinner piece of sheet will suffice. Maybe as thin as 22 but really I'd go for 20 instead. Without the formed lip 18 or even 16 but certainly not any thicker than that.
If you have any interest in learning to form sheet metal this would be a great project to start. If my wild guess at dimensions above was correct, you could start with a piece of 20 gauge, cut it to 22 inches square, and cut an undersized opening in the center:
Use something like a 12 inch adjustable wrench (basically, something with a deep jaw) to get the bend started along the inner dash-dot line. When you get into the corners you'll find that they don't want to go up. The metal needs to stretch there. It's not hard to do: just hit it. In a small-radius corner like this a small "hammer" will be needed. Even the handle end of the 12 inch wrench might be adequate. Alternate between stretching (hammering) and bending (with the wrench jaw) and soon there'll be a lip bent over to 90 degrees which will stiffen the part substantially. You'll get the hang of it. Even if you didn't... you'd probably be into it only two hours at the most, and that two by two foot piece of 20 gauge should cost no more than about $10 (maybe $60 to buy an entire 4x8 sheet).
edit: the above could be formed from 18 gauge too, but I'll tell you from experience, forming it in 16 gauge or thicker would be a LOT of work.