Would Cortes not win some early victories against some small coastal tribes, capture him a woman that speaks a couple local languages, learn who the major power in the region is,

Yes

start gathering allies among the locals who’ve lived under Egypt’s thumb and would like to get a piece of that highfalutin pharaoh,

This is where things break. Do you know enough about the different people living under the Pharaoh's rule in the era you're talking about? I don't. Thus, I cannot say whether Cortez would manage to find enough support to march to the capital, be hailed as the incarnation of some god, or whether the translator would try to warn everyone that the conquistadors are a bunch of pillaging pirates that should be killed, with them being none the wiser. When you're a stranger in someone else's land and everyone absolutely hates you above all else, you can't even breathe without fear of being ambushed. Sure, they have these frightening tools that are louder than thunder, create foul smoke and kill people from a distance, but those things won't protect your back from being shanked

Or, let's throw a more recent perspective: USA vs. Taliban, 2001-2021. One side has drones, aerial supremacy, satellite imagery, smart missiles, aircraft carriers. The other has mostly just small arms, weapons that at most, need to be mounted on a pickup truck, no tanks, no planes, it was a bunch of fanatics using guerilla tactics. USA never managed to fully beat the Taliban and, after the end of the withdrawal, it didn't take 2 weeks before they seized power.