You start the scenario without any actual or expected source of food. You could produce some fishing boats and go looking for food, but you have no way of protecting them. Alternatively, you could send some villagers to look for food. The key to this scenario is to start fishing immediately, and to save your entire initial food stockpile to enter the Tool Age. Explore just a bit with your villagers, but you don't find anything, so just build a Barracks, because you don't see a good place to build a Storage Pit or a Granary. Then research Tool Age, and collect wood with all your villagers.
Work up to 5 or so fishing boats, and in the Tool Age, 10 or so villagers. Pump out the warships until you have 10. Fear not, you will be attacked soon, but probably only by warships, especially since you will shortly have 5 Axemen, 5 archers, and several Towers. If an invasion force were sent, and did get through, it probably wouldn't do much at this time. (Note that both Yellow and Brown will send transport ships to whichever continent you happen to be on, but they must *see* a unit or building of yours *on* the land at first. If you place a row of Scout Ships a bit south of your town such that any enemy ships will be engaged before they can see your dock, then this means you won't have to worry about enemy transport ships at all; they simply won't be sent, since the enemy doesn't know that you are on the northern continent. Note that even enemy fishing boats can "see" your land units and buildings, so make sure no fishing boats pass through your row of Scout Ships either.)
When it looks like you have plenty of warships available to beat off any attack, send one of them to explore your coastline. Later, produce a scout cavalry and explore the rest of your island. There is an awful lot of stone on your island, three times as much wood as you could ever use, and a fair bit of food, but no gold. Supplement your fishing with farming and hunting.
By the time Brown starts attacking with Bronze Age warships, you should be able to fight each of them at least three to one. Research Bronze Age as soon as soon as your Tool Age force is as described above. Produce a force of 10 chariots, including archers, and a couple of priests. This should put you close to the population limit. You will be disbanding your Tool Age units soon. Avoid spending any gold unless absolutely necessary. Use standard low-gold procedures.
It's time to crush your enemies. Red is still in the Stone Age, and they don't have an economy. Dump 10 chariots on their island, and they are history. You find some gold on their island. It's not enough to fully finance an Iron Age army, but will get you into the Iron Age, with a fair bit left over to cover several key expenses. Yellow is fairly strong, but a bunch of chariots, and a couple of priests and catapults, should do the trick. You find a lot more gold on their island, and maybe even some stone. You now won't need to do any trading, so feel free to waste any and all enemy docks. Brown, however, is a different matter. If they attacked you in force with their Iron Age technology, they could crush you easily, but they are pretty passive.
Unfortunately, that last bit is mostly theoretical. Landing on Red's island seems to trigger a strong response from Yellow and especially Brown. Expect to face invasion after invasion, and Brown Triremes and Yellow War Galleys. The landings seem to go to Red's island. It's as though the AIs are reluctant to attack if they think you are strong, and they head for your weakest point, which is the small force you have on Red's island. Still, you would probably rather have them attack your best, mobile units instead of your Axemen, villagers, and buildings. Therefore it may be a good idea to leave a token force on Red's island while increasing your defenses at home, especially if you can sink their Transports on the way in. One thing that you can count on is that, once the AI decides to attack you, it never again changes its mind.
The big problem with these invasions is that they effectively interdict the gold on Red's island. A related problem is that you want to knock out Yellow before they use up too much of your gold, but you are too busy fighting off the attacks. There is only one realistic solution to these problems, and that is a massive shipbuilding program. Get at least 15 War Galleys, maybe even 20. About half of them should be allocated to defense, but you now have enough warships to mount an effective attack. You have probably run out of convenient fishing spots by now, so disbanding your fishing boats seems reasonable, and you might want to get rid of your Tool Age units as well.
Yellow puts up significant resistance, but just keep sending your War Galleys over, as though on a conveyor belt, and send the damaged ones home for repairs. In the meantime, hit the attacking Brown Triremes and Transports at five to one. You really don't want to fight their troops on the ground. Keep shooting at the Yellow dock. This approach will deny you a trade route, but it is more important to stop their shipbuilding. Keep picking off the repairmen, and grind Yellow into hamburger. The AI is absolutely committed to keeping its buildings in good condition, which allows you to eliminate all their villagers conveniently. When you do eventually land on the Yellow island, you probably find that they have used up all your gold and stone. No matter; you should have a large reserve of stone, and you can get by without a lot of gold.
Once Yellow is out of the action, you can turn your attention to Brown. Brown should be out of wood by now, and that means no more ships, and that means no more invasions. You can now strip mine the gold deposit on the Red island. Unfortunately, you can't get Triremes, but 15 or more War Galleys are quite enough for your purposes. You can grind up most of Brown's troops with your warships and land a couple of catapults to take out their Towers. Grab the second Artifact and bring it home to win. There's no need to wipe your enemies out entirely.