Oh boy, LOTS of information to convey...
First look at this thread for one approach (with a Honda 2000i) for some ideas.
You CAN accomplish what you want here but some planning and variable to consider and manage. Fresh air in and exhaust and cooling air out plus sound and vibration insulation are the primary ones.
To manage some of this in one swoop, and if you have this generator, I would recommend this solution.
The EFX3 exhaust system is for all of the Yamaha EF3000ise(b) series generators and the SDMO iPRO3000E (UK). Included are the custom molded polycarbonate shroud with riveted-on collar, 32 inch long, 5 inch diameter aluminum tube, worm clamp, and 6 self-tapping screws. Full color instructions are provided.
If not I would recommend that you get one of the generators identified in that link. The little exhaust collector manages the exhaust and ventilation in one package and requires only a 4 inch exhaust duct. Otherwise you are gonna have to manage a very hot exhaust and some ventilation and make up air separately.
Then you have to provide makeup air with another duct in the floor or somewhere to match the 4 in exhaust as a minimum. I would suggest some kind of insulation for noise and padding for vibration (the plywood may be enough).
What you want to do can be done, but the above is the easiest way to make sure the heat doesn't get away from you.
Plenty more to say, but this is a start.
Also, you may want to make sure about that much weight in the rig. but that is another issue.