@docbud
I suspect you weren't outnumbered, but outmaneuvered. Tactical combat is pretty complex in Civ5, that's why AI is notoriously bad at it and human players have huge advantage. However, if you don't use your units effectively, you give up on this advantage. Your science per turn is decent and on prince level that should be enough to defeat any AI opposition. Fall patch increased the number of units AI spams and even made it better at combat, but it's still very very stupid and easy to deal with if you're prepared.
Do you by chance have a save file?
As for exploring, expanding etc - no circumstances can prevent you from doing that if you really want to. Not on this level, not even on deity in most cases. Besides, two games in a row - it's a pattern, not circumstances. These things are game breaking. Extremely, extremely important.
You can't get wrong with Tradition, so stick to it.
Start with scout - monument - worker - shrine - granary - archer - settler - library - archers and at least one more worker until you finish Philosophy then NC. In second city build shrine and granary first. Research techs that are needed to improve luxuries, then Archery, then Writing and Philosophy (for Babylon obviously Writing first, then luxes techs, Archery, Philosophy). Improve luxuries asap and sell them for your neighbors (that's what exploration is for). When you have 400

rush buy a library in second city and start working on NC in the capital. After you finish NC, expand to 4 cities. Try to sell more luxuries and strategic resources to buy a settler (500

) and hard build another one. If AI doesn't have any money left, build two settlers in capital. Also try to steal a worker from CS. This is solid start that sets you for the rest of the game. I would suggest something more balanced than sandstorm, though. Maybe one of the default pangaea/continents maps? They have a better distribution of resources and maybe even spawning points.
A city that can only grow to size 2 is a terrible city spot.
By the time Education is around, even the newest city should be size 7+. Oxford is in fact worth while (assuming NOT an OCC) to delay for quite some time so I'd expect that newest city to be size 9+ before it got around to starting to build the University. (In addition if one of your cities is really cash poor; can be bought with cash there)
I think you're missing the point. No need to convince me.
