Not true that bigger ones are always louder.
Quite the opposite.
There are a zillion models of the chinese generators.
They all look alike.
I have a middle grade one, northern.
Fairly loud, but the harshness is way down.
It would help to reduce exhaust noise.
I have heard some that inspired to homicide on starting up.
Those really aren't worth your time.
Intakes can be as loud as exhausts.
Harder to silence, but copy a good car design.
It might be possible to damp some of the sheet metal or other metal to metal points.
Adding an exhaust system is easy tech.
You can reduce back pressure with good design and larger openings.
Too large a pipe can create bass resonance though.
There is a lot you can do in this area.
You can flow 400-500 hp through a 2.5" pipe and muffler.
I have a 400 ci running through a single 3.5" pipe and muffler with parallel cats.
You can do a generator exhaust.
Check first for more silent stock mufflers.
Usually the generator mufflers are the quiet ones though.
Briggs mower engines and sears have quieter mufflers for everything, often listed as generator versions.
You can always do better, but not as compact.