From the HoF, the dates (#1 to #10) range for each victory condition (emperor, normal speed, standard size):
Conquest 940AD-1290AD
Domination 775BC - 1270AD
Space Colony 1685AD 1820AD
Time 2050AD (that one's mine, btw

)
Religious 450BC - 1824AD
Diplomatic 1270AD - 1680AD (that one's owned by AAA

)
Cultural 1530AD - 1824AD
Note, in the HoF you have to play without unrestricted leaders, and with a random generated map. You pick your opponents and map to make the VC you choose as easy as possible. You then regen until you find a start position that is as sweet as it gets. And then you quit after 20 turns if you find Toku as your neighbor, and invest your time in a game with better chance of fast finish.
So the times in HoF should be used for comparison purposes only. Your milage may vary.
Domination looks like the surest way to a fast victory. Everyone is pretty good at it. The game conditions don't really hurt Domination VC very much if at all. If Domination is hindered, it is by geography... that is, putting a lot of land behind impassible terrain so you need to overcome a barrier to claim it. Emperor level AI are not generally a barrier to Dom VC, even with unrestricted leaders. Granting them a tech advantage enough to slow down Dom VC usually has the effect that the game is unwinnable, in my experience. The large number of coastal mountain ranges leads me to speculate that AI will be only approachable from one route with probably a well-defended position at the inlet... at least if Dom was intentionally plagued. But then so is Conq, even more so.
Religious VC is probably the only one that could compete with a Dom victory if special actions are
not taken. Religious VC, though, is the easiest for the mapmaker to screw up, and having all Bhudist opponents and requiring us to stay Hindu is one way to do that, but probably by itself does not uncheese the AP. Letting them start with Theo probably does, though.

Aggr AI slows down both AP and Diplo VC by requiring an additional +2 modifier (and then overcome the negative religion modifier or wait until everyone gets Free Religion).
So frankly, in this set-up, I don't see Religious being competitive with Dom.
If Dom/Conq are made harder, and we know Relig/Diplo are made harder, and we doubt Space could be competitive in any imaginable scenario, we are left with Culture VC as our choice. It leaves open the option of AP vic if that appears do-able, however unlikely that eventuallity.
So what we need to know is whether
Domination is made
so much harder that a decent (1600-ish)
culture game could beat it or not. And there is no way to answer that for now. We know that rushing is out of the question, so even a Dom VC requires a build-up phase.
The difference in dom/culture are very many, in tech and in settling and in diplomacy. So the sooner we can decide between them, the better off we are. But we are best off if we guess on one -- and guess right. The REX strategy is good for both at this point, with the difference being that a cult VC only requires 3 REALLY good cottage cities and a GP farm. The other 5 cities can be crap... just have to build/whip temples, and maybe missionaries there. Need four or five religions... we have one, and Judaism, Confu, Christianity, and Taoism are still available and we should be able to get at least two or three of those founded. We could also capture a Bhudist city or put a non-religion city roaded to Toku's roads and wait until spontaneos spread gets us Bhudism (though this makes us vulnerable to AP loss). So getting the religions is not a problem. The problem is that Toku is not the nice peaceful neighbor you would like, so we have to kill or cripple them anyhow.
Dom VC is more straightforward and less luck-dependant. We only settle good cities during REX, tech to military advantage, and start killing. Weird stuff happens with the land threshold with teams, though. And Neil could have made it impossible to win militarily, though I doubt he has. No point speculating on that.
So... we can see enough to know a decent cult vic is possible. We won't know if a Dom VC is even possible (or how long it might take) until we see (or can guess) about 60% of the map. Its a coin-flip with the knowledge we have now.
Our problem is that the early game in Dom and culture are somewhat mutually exclusive. We do not want to found religions if going military, but do if going culture. Tech path is crazy different, and settling priorities are different. We could switch from one to the other, but not expect any laurels if we do so. Some teams will guess correctly.
I'm leaning towards culture just because... we started with AH (no horses) and teams that started with BW (yes copper) are way ahead in the Dom race, but in a culture race this difference is inconsequential. Pick culture and hope that's the right call. If not, switch strategies and hope for middle of pack finish.