AI will 'cheat' in higher difficulties to make it harder for you. What difficulty are you trying to play?

Playing at Prince level

Yeah, so I believe that Prince is the baseline (I could be wrong) but the AI does get some buffs to make up for its terrible AI. Basically Civ will give the AI various buffs so that it doesn't just get left in the dust by a human player, and these buffs are something you will have to learn to overcome.

Prince+ gives the ai buffs, and I believe Warlord and down weaken the ai

At Prince difficultly, the AI doesn't get any bonuses to production. Chances are that the AI just has cities with more production than your cities.

Ok, but how do they out perform you in production in the first 10 turns? The game has just started out and they are outproducing me in less than 50 turns. Makes no sense. But hey, I guess it's all good. lol

This may be a few years too late, but just in case anyone else now or in the future has the same question, I'll give it a go...

First off, the term AI is a bit of a misnomer--it's a computer. The computer players don't learn or adapt in any sort of machine learning way. This may be a slight oversimplification, but it's basically just a long series of IF/THEN statements that determine their choices. Difficulty does nothing more than give the computer players buffs to make competing with them harder.

Now to actually answer the question, it probably just boils down to start location. The players that are beating you to wonders very early on likely had a good start location. For example, take a Grassland Hills tile with Woods and Spices. The BASE yield for that will be 4 Food and 2 Production, let alone any future improvements. Now if you had a couple other tiles nearby like a Grassland Hill with Rainforest and a Plains Hill with Woods, you're looking at just 3 tiles with some serious Food & Production yields. This will cause the city to grow quickly, then work more tiles that not only grow quickly, but also have high production. Start location is everything when it comes to Civ. It's important to settle in places during the early game that you can get high yields without having to train builders to improve the tiles, so that when you do finally train builders, you make those tiles even better. Avoid featureless tiles; look for Woods, Rainforests, and Marshes. People can turn their nose up at this all they want, but I literally restart every game until I get a start location I'm happy with. It doesn't have to have a Natural Wonder nearby or anything like that (though that would be nice) but as long as I have 3-4 tiles with 5+ total yields within a 2-tile radius of my desired city location, I'm happy. Ideally you'll have 1 or 2 Luxuries and maybe a Bonus Resource nearby to help with that, and potential for Strategic Resources as well (they're pretty easy to predict when you know what to look for).

Hope that helps!