Test run:
1v1, epic, large Pangaea, no huts, no events.
Random civs.
Capital: Corn, Clams, 2 bare hills, and one flood plain.
Turn 30:
Initial scout went around shore line and found enemy turn 30. Scout took forestry promotions (and tries to end every turn on forest).
Enemy is about 40 tiles away. Normally i would scout a good sized radius around my start, but you mentioned sometimes you don't find the enemy quickly, so i was concerned and sent first scout around shore (generally safe to hug shore). Fought 3 barb animals along the way, each time i was on at least forest/jungle. Noble gives you 2 or 3? free barb wins, so not much risk.
Capital has a work-boat on fish and worker 3 turns away. After worker build warriors to happy cap (usually ~3-4 warriors). Micro if you can to finish last warrior on the turn city grows. Keep last warrior in capital (for happiness) and scout second city site with rest.
Tech: Started with fishing and hunting (Pericles), got agriculture (for corn in cross), animal husbandry, and mining is 5 turns away.
Will farm the corn, and mine the hills, and get bronze working after mining.
Warriors will scout around capital to find horse and/or bronze for first settler.
Scout will scout around enemy capital and keep an eye on him.
Turn 59:
A warrior finds horse 8 tiles SE of capital. Fortify on hill nearby.
Final warrior finished and fortify in capital.
First settler started this turn.
No copper for me so far. (Found copper a couple turns later about 10 tiles east of capital).
Enemy has copper maybe 7 tiles east of his capital.
Scout has revealed much of the enemy land and has forestry 2 promotion. Will probably circle back to his capital to check on his expansion status.
Other warriors are scouting/healing as needed.
Capital is working 2 grassland mines, corn, clams, and unimproved flood plain, worker is 1 turn away from chopping forest hill into first settler. Will mine the hill after and then start road to horse.
3 turns away from wheel (pottery next).
Turn 115:
Founded horse city 2225bc what is that turn 70-80 or so in epic?
Kept tabs on enemy with scout.
Recently settled my own copper. Enemy also settled third city on copper.
Switched to slavery when i hooked up horses and whipped built and whipped in second city 3 chariots pretty quickly.
They are about 8 turns away from enemy. So far only seen warriors in their territory.
7 Turns away from horseback riding.
Got library and 2 scientists working in my capital, 6 turns away from first great scientist in capital (Pericles helps here)
Probably could settle more if I am not going to attack to win, but i already started on horseback riding and found elephants near my copper
Kinda committed to going horse archers early then elephants if they don't end the game. You probably should delay horseback riding until you know you can get his strategic resources away from him with chariots.
Now if he had gone pyramids no way he has 2 cities and more defense.
My cities
His cities
Turn 123:
Ninja his copper (AI city settled on it, but not connected to empire yet) with 3 chariots vs 1 warrior. A player probably doesn't settle on copper, so it would be easy to disconnect.
Got horseback riding and three decent cities to pump them out.
Start on iron working just in case he has that in his territory or you can just blow up every mine.
So overall pretty good position. Like i mentioned in the turn summary I would probably tech a little different to stay flexible, but overall you are in a strong position. I didn't micro great, so you could do some run throughs against the AI and get better timing. I had 3 cities before i hooked up horse and didn't expand after that (kept making chariots). You could easily expand 1-2 more times or go pyramids yourself while the enemy is distracted by your chariots.