There is one thing you got somewhat wrong.
The YF-22 first flew in 1990. Not only was there a 5th generation prototype airframe (actually, there were two YF-22, one with Pratt engines, one with GE), there was yet another 5th generation fighter prototype competing with it, the YF-23 (also built in 2 version, with PW and GE engines) in 1990.
After that, there was the very long and politically loaded process of deciding how many aircraft to procure, what bells and whistles would be required, desired, or considered too expensive, and so on.
Do not mistake an engineering process for the political mess that followed.
At present, what a 6th generation will be is fuzzy, how can we reliably anticipate the technological developments (capabilities) and the future requirements (demands)?
Are planes going to still be manned? From the 4th generation onward, we already saw plane that were limited by what the pilot could endure; remove the weakest link and planes that could have higher than 9 g sustained turn rate become possible.
All we know is that a 6th generation is going to be formidably expensive.
Look at the production volume for the following first line air superiority fighters:
F-15: more than 1000
F-22: 187
Will the 6th generation be something built in less than 30 units, which will be kept on the ground, in armored concrete bunkers because they are too valuable to risk flying in combat?
As to when, we know that the last F-22 just went out of the assembly lane. A fighter airplane is worn out after 25 years or so -- one can make them last longer if one does not fly them, but what is the point of having them is one is not flying them? This means the F-22 will start being retired in 2030. Which means the work (specification, first concept proposals) on a replacement will have to start about 5 years from now at the latest, so that it can start flying in prototype form in 2025.