Looking at the Americas, we have evidence of cultures with agriculture and pottery, roughly equivalent to Europe's Linear A, going back about 6000 years ago (4000 BCE). We have writing dating back to about 3000 years ago (1000 BCE), though this was probably delayed by much of their function earlier being usurped by quipu (which date back at least to 2600 BCE). This corresponds to the emergence of the first long term stable cities in the Americas starting at about 1500 BCE and the growth, about 1000 years later, of Teotihuacan, a true majestic city rivalling ancient Ur in size and influence.

So yes, that is an independent (but later) development of civilization, which I think endorses the idea that once the climate settled down after the intergalacial, our species was going to develop civilization on a fairly quick timescale (compared to biological evolutionary timescales), and that it wasn't lack of intelligence holding us up.