6500W at 120V = 54A. 6500W at 240V = 27.5A
Neither one is 4 times the rated amps at the running voltage, but probably plenty to get the compressor started. You just need to get that power to the compressor in a practical way.
Your compressor is listed as 4 HP. But 115V X 16A = 1,840W and that equals 2.47 HP. Many compressors have exaggerated HP figures.
Will your compressor start if you plug it into a 20A 120V household plug with no extension cord?
A 6500W, 120V generator can have a much larger breaker than 20A. A larger breaker to handle the surge amps might be a good method and the generator has the capacity. But the internal wiring in the generator might not handle a larger breaker on that circuit.
If you rewire the compressor for 240V and use a 20A 240V breaker, you'll be doubling the number of watts to the compressor and still be within the generator's watt rating. This would make more sense than a 50A breaker on the 120V side. And it would only require #12 wire. What size breaker is on the 240V generator output?
See if you can find a 12-3 extension cord and 240V plug to match the generator plug. Or hardwire it in. Keep the cord short.
If the generator is permanently mounted near the compressor you could use stranded wire in flex conduit and hardwire it through a switch.
Large capacitor start kits work well on air conditioners. I did it on one one of mine to get my generator to start the unit and it worked. But I have never tried it on a compressor. You can get them at Grainger.
I suggest just altering the motor voltage first and going with a 20A breaker on the 240V output.
During emergency power outages you probably don't need a large compressor. So you could always buy a cheam an electricain and ran apo small one to use for filling a tire or something. Sears makes a 1hp oil lubed unit with an iron compressor that can be had for $100. on sale. I have had one for years and they are great. Paid $69. for it at some blowout sale and felt like I was stealing. There's no way my 5 HP compressor will ever run from my 2000 watt diesel emergency generator. And that's OK.