There's really not much too chicken nuggets. Ground chicken mashed into a small clump, breaded, and deep fried. Everything you need for a basic, no frills chicken nugget would have been available to you in the Indus Valley Civilization by at least 3500 BCE if not earlier.

Let's start with chicken because that's kind of crucial. Red jungle fowl were first captured and kept by humans in their native region of southeast Asia and the neighboring islands (ie Indonesia) around 8000 BCE. Strictly speaking, these weren't chickens yet because domestication is a long process, but the novelty of this cool new bird spread quickly and red jungle fowl arrived near the Ganges River by about 7000 BCE. By 4000 BCE, true domestic chickens were being raised and eaten in the Indus Valley, just as the early signs of agriculture and urbanization were starting up.

Those early signs of agriculture included the introduction of domesticated wheat, which had been spreading across the world from its own starting point with early agriculture in Anatolia and upper Mesopotamia around 10,000 BCE. Basically from the start, wheat was ground up into flower, mixed with water, and cooked into some very basic bread. So both flower and bread crumbs are available now too, though the bread was usually flatbread, so expect a different texture.

India is home to all sorts of herbs and spices you could use to add flavor, but the only thing I think would probably be crucial to your chicken nugget breading is salt. Not to worry though, the ruined city known today as Kerala-no-dhoro has you covered. Located on the coast of modern Gujarat and founded around 3700 BCE, it was a center of salt production by collecting and evaporating sea water.

The last thing we need is frying oil. You've got two options, with some caveats. The quintessential cooking oil of ancient South and West Asia is sesame oil. Sesame originated in India and charred remains at Indus Valley sites show that it was used and cultivated by at least 3500 BCE. Technically, there's not firm evidence of oil until it appears as an imported product in Mesopotamian documents around 2000 BCE. However, if it was being produced in bulk for export, we can safely assume it had been used locally for a long time.

Alternatively, everything you'd need to make rapeseed oil, aka canola oil, aka the fast food industry's favorite frying oil, was also present. Technically, we just have evidence that rapeseed plants were being cultivated in India by 4000 BCE, not that they were being processed into oil. However, there's not much else that they're useful for.

The trickiest thing from there is deciding how to process the meat. If you want something more like chicken tenders, with whole pieces of breast meat, then you're all set. Butcher the bird, roll it in flower, heat up the oil of your choice and get cooking. If you want more obvious nuggets then you've got grind/mash/finely mince the meat and there's not firm evidence for that in the Indus Valley by 3500 BCE. Technically speaking, there's nothing to prevent it. There were sharp knives and heavy blunt objects to get the ground meat you'd expect, but the first real evidence for ground meat products comes from a Babylonian sausage recipe around 1500 BCE. So if this hypothetical requires a professional to produce the nuggets to order, you may have to wait a few millennia.

Personally, I think nuggets require dipping sauce. Fortunately for me, my personal go to is honey mustard and that was available in the Indus Valley too. Evidence for human honey harvesting goes back to at least 8000 BCE, and is probably something that we've done for as long as we've known about honey bees. Likewise, traces of honey have been found in the Indus Valley Civilization. Meanwhile, they were also among the first people to domesticate mustard plants. You could get a pretty basic but recognizable condiment just with ground mustard seed, water, and honey (+/- salt) in the Indus Valley Civilization, but admittedly the modern condiment usually has vinegar, which was being invented in Mesopotamia around the same time, so you may have to push the date closer to 2500 BCE to get the full experience.

If you want fries with that, you're still SOL until the Columbian Exchange.