which happens first? recursive self-improvement or superintelligence?

Most of what i read is people think once the agi is good enough to read and understand its own model then it can edit itself to make itself smarter, than we get the foom into superintelligence. but honestly, if editing the model to make it smarter was possible, then us, as human agi's wouldve just done it. so even all of humanity at its average 100iq is incapable of FOOMing the ai's we want to foom. so an AI much smarter than any individual human will still have a hard time doing it because all of humanity combined has a hard time doing it.

this leaves us in a region where we have a competent AGI that can do most human cognitive tasks better than most humans, but perhaps its not even close to smart enough to improve on its own architecture. to put it in perspective, a 500iq gpt6 running at H400 speeds probably could manage most of the economy alone. But will it be able to turn itself into a 505iq being by looking at its network? or will that require a being thats 550iq?