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The greek fakkitry period
It is a little more accessible and easier to focus on Achaemenid and Ptolemaic Egypt because you don't have to go to the trouble of learning hieroglyphics. Ancient Greek and cuneiform will do you fine for sources covering those periods.
The language barrier is the greatest challenge. I'm Indian and I'd love to be a scholar in ancient Indian history but it's such a difficult task because I'd need to learn Kharosthi Sanskrit just as a basic requirement. Having to master obscure languages from thousands of years ago just to get started is tough.
On the other hand you can cover Roman history so easily because so much of it has been translated and besides Latin is not difficult to learn since it uses the exact same alphabet as English, and since there's no shortage of places you can go to learn Latin.
Also at summer school this January I took an undergraduate class on ancient Egypt & west Asia and it entirely focused on the African and Achaemenid periods. The only European bit was the Persian invasions of Greece and the life of Alexander.
They fukked around and found Apocalypse