I'm not even far behind, so that feels like a fail. The Turn 100 demographics update was technology - I'm last but only two techs behind first.
Early exploration - found a culture ruin on Turn 4, so I have to choose the first social policy on Turn 5. No idea where any AIs are. No idea where any city states are. No faith pantheon. No idea where I'll expand. No worries - open Piety (god of the sea will be good - hopefully being two difficulties below deity makes up for the lack of a faith pantheon). Samurai finds Kabul soon after that - easy gold (tribute)! Scout finds Tyre (sadly, just having the world's strongest army is not quite enough to tribute). Continuing north, finds a tech to finish sailing - guess it's time to go straight into Optics (that's the quickest luxury at this point since I don't have a worker). Then, the scout finds Fuji and a pop ruin. Shrine just finished - one more turn to finish the monument and then start a settler. While building, I was already considering One With Nature, but that's an easy choice when God of the Sea is taken as the first pantheon on Turn 17. I take One With Nature on Turn 24 (second pantheon).
Meanwhile, I find a Persian scout near Fuji and then Persepolis not long after. Looks like I'm breaking another of the guide's principles - expanding toward the AI (not directly toward, but it's certainly contested). Samurai makes its way up there and steals a Persian worker on Turn 28 (plus a farm pillage)! I settle Osaka during the war, and Darius sends two warriors and an archer after it before asking for peace. I accept, and sure enough, bright red diplo modifier for coveted land. Darius got a bit of revenge by settling where I wanted my third city, so I made a nonsensical expansion near Tyre. At least it's coastal (Fuji isn't because I really wanted to settle next to a food tile and Fuji).
Samurai goes after a barb camp for Kabul. Slams into it once. Barb reinforcements arrive - didn't think it would be difficult, but I had to retreat (into water). Swam around a bit and really, really should have gone back to land. Instead, for speed purposes (rough terrain south of the capital), I stayed in the water. Almost all the way back when a random barb galley kills it. Immediately, I drop to the last place military (I had a scout and two triremes at that point, I think). Darius is still mad. Appease him a bit with 5 gold per turn. Later, I give him 5 iron. Didn't think that would be enough, but all green diplo modifiers now. All three of us are best buds (Pedro being the third).
Darius never got a pantheon, so I converted Persepolis (and Kabul). I think pressure should get his other cities fairly soon, but if I need to, I can send another missionary. Pedro built Stonehenge eventually and founded the next turn - guess I'm not supposed to convert his cities. Dido's also nearby - she has a pantheon but hasn't founded yet. Second missionary (after two mosques) swam northeast to city states - lucky a barb galley didn't pass by. It has converted Cape Town, but will need to be careful of barbs to get to Mombasa. Tokyo finally converted the turn after I bought the missionary (and I've since bought a mosque for it, too).
Social Policies
Piety - Opener
Piety - Organized Religion
Patronage - Opener
Piety - Mandate of Heaven
Piety - Theocracy
Piety - Religious Tolerance (Writing this reminds me that I need to send a couple trade routes to Pedro for God of the Sea. Unfortunately, I'm approaching the "grow" phase.)
Religion
One With Nature
Pilgrimage
Mosques
(likely will use prophet from finishing piety to enhance)
World Wonders
Mausoleum of Halicarnassus (capital Turn 100 - didn't have anything left to build that contributed to the overall strategy; even has a library already)
(in progress) Oracle in Osaka - started as a 28-turn build, but again, nothing relevant left to build (no library though - and this is my future science city). Chopping forests has helped, I might actually get it.
Turn 100 Screenshot: