It is quite doable as Babylonia, Egypt seems very difficult indeed.
Babylon's tech modifier is 125 and due to its unique power you can start snowballing much faster. Egypt's tech modifier is 145, the worst in the game next to India.
Babylon only has one core city (as opposed to 4-5 you can squeeze into the Egyptian core) but it's one hell of a city and your core population will count as double since you have only one city. Babylon also has the potential to be a triple holy city (Judaism, Orthodoxy, Islam), so with three shrines, Dome of the Rock and then things like Stock Exchange and National Bank and a couple joined prophets and merchants you can run 100% science basically the entire game even with inflation and a reasonably sized empire. You can also build a ridiculous amount of wonders in Babylon (you can only have 7 or 9 at the end game but that only counts the ones that are not obsolete. With the obsolete ones you can easily get up to 20 and they all provide GP points even after obsolete). So even with poor GP growth modifiers you can crank out great people at a very respectable rate. Also you can imagine how with all that culture wonders like Metropolitan will give a very nice amount of commerce. Also building Ironworks, National College and things like Hermitage, Babilu will also have godlike production and science.
Obviously you have to build tons of military units to deal with all the conqueror events so in my run I built the Flavian Ampitheatre right away. I settled two great generals in Babilu and built mostly units and wonders until after Iran was dealt with. But it's doable. You will lose a city here or there (Arabia and Iran will flip cities that you likely own when they spawn) but it's not hard to get them back. Just make sure that the Seljuks don't take any cities in Mesopotamia and in Turkey so that the Ottomans don't spawn.
To offset some of the overexpansion you may suffer in the later eras you can run compatible civics (I'd go for Democracy, Constitution, Egalitarianism, Central Planning or Regulated Trade, Secularism, and Multilateralism). But with a super Babilu and jails and courthouses everywhere and keeping your non-historical cities reasonably low in population, you can easily have an empire stretching across Egypt, Turkey, Middle East, Arabia, Iran and Transoxiana which should be enough to allow for a science victory.
Vassalizing nations that have similar tech modifiers and directing their research for tech trading purposes is also great. Byzantium and Mughals are perfect for that. But you'll have to gift them a bunch of techs because by the time they show up you will likely be much more advanced than they are. I was already close to the industrial era when the Mughals spawned for example.
The final piece of the puzzle, if needed, is to conquer the east coast of North America (New Orleans, Charleston, Washington, New York) and vassalizing the United States. They are your biggest competitor in the tech race and limiting them to Chicago plus the western half of North America and then directing their research will prevent them from beating you to it. In an unlikely case that Russia does well (it usually does poorly in my 3000BC and 600AD games), you can try signing some defensive pacts and getting everyone you possibly can to declare war on them. And use espionage to sabotage their production, to send them into anarchy through civic switches etc.
I did it playing on Regent and Epic speed.