Sure, but you would get the baby situation I posited years before what you're envisioning. You're skipping a bunch of steps. My hypotheticals (if they ever do happen) would occur way before your hypotheticals. Progress does not go in "Foomp" steps.
Everything goes in foomp steps if you condense time enough. Condense the last 200,000 years of human evolution to a couple minutes, and it goes 'Foomp', and the super foompy part doesn't happen until the last 2/10ths of a second with industrial civilization wherein the development of global networks compounds our collective intelligence exponentially, yielding unforeseeable emergent properties.
So certainly you would get the baby situation first, but going from manageable baby to astral foetus could potentially happen rapidly and unexpectedly as the rate of progress accelerates to unfathomable speeds, which is what's happened already in going from tribal man to modern civilization, and if you extrapolate that very consistent and reliable trendline, it leads to progress happening in a foomp step perceived as a foomp in real time. Really, all life is just one big accelerating foomp.
Imagine a massively parallel optical computer with the same transistor density as the human brain, the size of an olympic swimming pool running at the speed of light, and networked with 1000s of other similar computers around the world.
Foomp, superintelligence, you won't even be able to pinpoint the source.