I failed this botm; but afterwards I practised some (hof) deity games. I can now pretty reliably win the Liberalism race before 500 AD, and that's probably the key:The point is, nothing you have said here explains why you had so much tech at 500ad. Surely you understand, this is the question we are asking you, how did you get that? I see your screenshot has since been removed, but I recall that you had a multi-tech lead on every AI civ at 500ad, is that correct?
0. get 4-5 cities early...that's where I fail most of the time
1. beeline to either alpha or aestetics, via the most important worker techs, then do trade for everything you can get
2. research lit, drama or (better) CoL, trade for monarchy
3. built NE somewhere where you can run 4 or more scientists. GLib's too expensive without marble.
4. bulb philo. getting it first isn't mandatory, but it helps
5. trade for CS or theo
6. research paper and edu, 1 bulb should suffice. don't trade it away before getting Liberalism
7. bulb Liberalism with your 3rd scientist (only possible without machinery). If you did really well, e.g. with the help of an early infiltrated GSpy, you can instead steal/bulb/research your way up to Astronomy, then liberate either SciMethod or even Biology (didn't get that on deity yet, but SciM is definitely possible)
The good news is that in bts most AIs seem to favor the guilds-economy line over liberalism, at least if you already started researching lib when they get the chance. AI-AI wars help of course.
The bad news is that, no matter how large my tech lead is, the deity AI eats it up in no time, so that around Assembly Line/Radio/Railroad I'm once again hopelessly behind everyone. Maybe we'll learn in the final spoiler how you can keep up through the industrial and modern age...
Now what I still don't get is how UnconqueredSun managed to get that really huge tech lead over *everyone*. Normally I have 1 or 2 AIs very close behind me, and stuff like Astro/PP I can only grab before Lib with a major espionage economy (that's 2 GSpy plus at least 4 sci, only manageable with a philo leader...)
As for the WFYABTA issue, I hardly ever get it. Maybe it's because of the opponents I choose, which of course wasn't possible in this botm

In my experience, AIs which tend to get pleased very soon also tend to trade away everything. Mansa always does, except when building a wonder.