I thought I would share my own hypothetical situation, to expand on the Andes idea a bit more - if only to bring to attention how unusual their technological development has been.
You see, South America is the closest real-life analogue for this hypothetical student project with an 8 millennium deadline. It was settled at between 15 and 11 thousand years BC, and from that moment on there was very little contact with the north. Yes, Panama was technically crossable, and fishing ships made their occasional way around the Darién Gap, but it was very much a blockade for cultural and technological ideas. The Andean and Mesoamerican cultural spheres were not aware of each other; there was no Silk Road connecting the two. Roman coins have been found as far as Japan, but nothing of Inca origins have been unearthed anywhere near Tenochtitlan, or vice versa. They might as well be considered separate continents.
It commonly stated that this isolation would be a pure detriment for technological, which it would have been to some extent, but it does not the end of the story, for Europe has been settled by modern humans for at least forty thousand years. The Americas achieved all the technology they did, in a quarter of the time.
I am going to take the southern half of Peru for the base of my island (which is where the historical cultures in this answer lived), and then make some tweaks to support every stage of civilisation even more than the region did historically.
Norte Chico is the oldest civilisation in the Americas and, within a rounding error, the oldest in the world (sharing the #1 spot with Sumer). The earliest cities were formed around 3500 BC, so eight to eleven thousand years after the settlement of the continent - but only five thousand years after evidence of the first settlements in the area (dated at 9000 BC). I'm going to be generous to myself, and say that my island could achieve a Norte Chico civilisation around the year 5000 of the experiment, if I do not make any changes.
But what if I did? You see, it is indisputable that the ocean was very important to the Norte Chico civilisation. They sailed out to the open sea, slew blue whales (the largest beasts on Earth), and made stools out of their vertebrae.
In the seventies, the scientist Michael Mosely went further; he theorised that the civilisation had maritime origins. He did not just mean that the cities were founded by fishermen, which some theories about the settlement of the Americas already stated, but that fish and other seafood was the main source of subsistence for the entire culture. He theorised that the Norte Chico people did not make extensive use of agriculture at all, unlike any other cradle of civilisation on the planet!
Obviously this theory found much opposition in the scientific community, though much like how the equally interesting and unlikely Phantom time hypothesis forced historians everywhere to challenge their assumptions about the happenings in the Dark Ages (or indeed their very existence), this mad idea coerced many scientists to pay more attention to the Norte Chico civilisation to try to disprove it, which finally granted them some more attention over the more well-researched Inca and Wari empires in the region.
Wiseman acknowledged the role of flax as an agriculture product (to make fishnets of), and when further research found that the inland cities were more populous than the coastal ones, his theory became more discredited. Still, it was appearing in scientific literature as late as 2005, so, to put it boldly, if the scientific community seriously considered this idea for thirty years, I think I could have a society based on fish in my little alt history :)
So this is the alteration I would make: put some extra reefs and other hotbeds of marine activity in the range of the Norte Chico people. Make it a bay crawling with fish and algae, and increase the size of it. A hunter-gatherer society could quickly become prosperous there and found villages and cities to support a population capable of extracting it all from the sea, much like how population increased in the Indus, Nile and Tigris valleys just to farm all that fertile soil. Slowly, the fishermen would discover how to farm the flax for nets and develop irrigation systems while they're at it.
Now, at some point the fish will run out, at which point the budding civilisation should pack their things and move themselves and their knowledge of irrigation to more fertile grounds, which Norte Chico did historically. But in this scenario, I should have moved up their flourishing period at least a thousand years, thanks to the abundance of fish. So I have agriculture in year 4000 of my experiment.
This is all I know to write for now. I think I will expand this answer in the future, but as it stands, it should provide some ideas for alternative civilisation budding methods, and the teacher does reward creativity so I should earn some points with this :)