1) there is limit to how fast AI on silicon can get. At one point, the code cannot be optimized anymore, the transistors cannot be spaced closer together, the electrons cannot jump any faster. So AI almost impossible to get smarter above their optimization cap, which we are actually pretty close to already.
2) You can not iterate infinitely in the physical world. Everything has a time cost. AI cannot iterate faster than the time it takes to print out a new chip. Nvidia at its fastest takes 1+ year to design and release a new version. Do you know how many times AI generally iterates to make a tiny bit of progress?
AI cannot build infrastructure faster than its robots can move bricks. It cannot gather real life data any faster than its Chinese-made lidar is capable of. So AI basically currently has no power over the physical world, especially in the deindustrialized West.
Sam Altman Thought is Dead On Arrival.
If the technological singularity is to arrive, the civilization most likely to achieve it first will be China at this rate, because there is still the industrial base to actually build things and test the wondrous new inventions. It would also be the most likely society in which the benefits might actually be transmitted to the general population rather than being locked away behind paywalls by neo-feudal tech overlords.
Now strictly speaking, the concept of the technological singularity originally meant that life after the singularity could not be predicted by people before the singularity, similarly to how a black hole singularity is not understood by modern physics as the mathematics of modern physics seem to break down. It could be argued that the invention of agriculture was a technological singularity too as hunter gatherers could not possibly have foreseen or understood some of the developments that occurred as a consequence afterwards, even if they had understood that agriculture would provide more food. Things such as skill specialization, complex societies of millions of people, modern technology, land ownership rights, mortgages, fianancial derivatives, etc... all flowed from the ability to have surplus food to enable people to do more than survive at a subsistence hunter gatherer level, and all would have been difficult if not impossible to explain to a pre-agricultural era hunter gatherer. At best explanations would fail to capture the true nature of the thing and it might seem fantastical magical stuff like flying around in shiny birds (airplanes). By analogy, the advances of ASI in a singularity scenario might so completely overturn the economic and social order that what comes afterwards would be unrecognizable or like a fever dream.