In 300ad, I finally feel qualified to post in this thread.
We can see the multitude of Barbarian (Pict) camps, thanks to English explorers. In fact, we had sent a unit the long way around to explore, but last turn the elite Gallic Swordsman, fortified on a mountain, was killed by a sole conscript Horseman. The Horseman didn't even have a scratch.
This despite our possession of The Great Wall.
The very next turn, we would receive our second Mediaeval tech. So the timeframe for this spoiler thread is very narrow!
To compensate for the relatively poor starting position, we sent early harassing forces west and east/south. This proved to be an excellent gambit!
Our Warrior in the south found Rome and captured 4 Workers, killing two Roman Warriors in the process, and then continued to make contact with the Iroquois and England.
The Archer we sent to the west fared even better. Carthage was quickly discovered. They had Bronze Working, but hadn't built any Mercenaries yet, so we attacked and seized their one city! Five slaves, one rival eliminated, and an excellent location for the later Forbidden Palace was the result.
Our now elite Archer continued west, found Ivory, bypassed a hut (better have a civ with scouts pop them and maybe get a tech for us!), rounded the lake and made contact with France. Despite a good location for their capital - and they already had founded Orleans, too - the French were hopelessly backward and again this was a civ with only Warriors for their defence.
Five turns later, France was no more.
All this early action left me with an empire where the sun always shines, ie hopelessly streched from west to east.

But with slaves aplenty the long and winding road to connect them all was a matter of time, a task almost completed by the
end of the QSC date.
Meanwhile, my building strategy included the Pyramids, which was completed by Entremont in 1025 BC.
Luxuries were hard to come by but by 1000 BC we had 3 of them: Wines, Gems and Ivory.
Map in 1000BC
Preparations for things to come continued with the empire's switch to Republic in 650 BC, and the completion of the Forbidden Palace by Carthage in 550BC. By then Iron (near Paris), Horses (near Carthage), Dyes (near Greece) and Incense (in the far west) had already been connected. Our cities were growing and started on the production of the Celtic UU, the Gallic Swordsman.
In 490 BC, the time was right and we attacked and destroyed the Roman city of Pisae, starting our Golden Age! We were all set to deal with the AI's one after another, especially when Vincingetorix appeared and built the Great Library.
Unfortunately, the Aztecs had other plans and sneak-attacked 3 turns later, destroying our Ivory connection (it took me quite a while to realize this, since the joy over the new war compensated the luxury lost! But it was finally hooked up again 18 turns later .... I really wish the game would give a message in such a case!)
We turned to their neighbours for help and got Japan, Greece and China in on our side. The first two sent very little aid, but China did a great job and continued keeping the Aztecs in check long after the alliance expired.
Yet the need to fight on two fronts hindered our attack on the Romans. Orgetorix emerged to construct the Colossus in our only coastal city, Furs (tundra town) were connected, we entered the Middle Ages in 250 BC and still our Gallic Swordsmen could not make a lot of progress.
In 210 BC we finally managed to converge on Rome, and take the capital. After that the war was virtually won, and we had no trouble taking the remaining Roman cities.
In 150 BC, we aquired our first Mediaeval tech from the Great Library: Monotheism.
Map in 150BC
We continued to nurse the Romans for elites, making sure we conquered towns instead of destroying them (they had no culture at all) and Cunobelius emerged to make our first Army. The Great Wall was finished by productive Alesia (why not), and finally in 130 BC Rome was gone.
We immediately regrouped to deal with the Iroquois next. They had had an excellent start, but soon ran out of land. With the use of the Army of Cunobelius (3 Gallic Swordsmen), the Iroquois capital was quickly taken ....
Map in 300AD
-----
Edit: Forgot to mention, Carthage finished the Hanging Gardens for us in 250 AD, then started on the Heroic Epic (due in 330 AD).