Did indiginous indians possess such knowledge to cut, vitrify, mould and manipulate quartz based rock to that sophistication?
Did they need to build out of quartz based rock at all?
Lots of examples of poorer quality work in Peru being made out of softer stone, so the material was clearly there. Yet quartz rock was the material of choice.
Extremely difficult to work with. Must have had a specific purpose.
Did the Egyptians as we are taught about them in school know the mathematics, stone building art, along with knowledge of vibration, resonance, material properties, etc to build the Great Pyramid?
Again you decide.
Your reasoning is getting kind of circular here. You're using the assumption of things that haven't been proven yet as proof of their own existence.