The AI starts with two settlers, four workers (IIRC) and a 40% discount so it's normal to fall behind at the beginning. Just accept it. You catch up by getting more contacts, monopoly techs and smart diplomacy. And, of course, through the

Don't hesitate to pay gpt for techs, if necessary. Especially if it opens up 2fers.
In vanilla, there are two basic techniques for catching up early. One is to start with BW, and run a minsci on IW. Mass upgrade warriors to swords and go bash some heads. A civ which starts with Alphabet is more certain to leverage. In this case, min (or maybe max) sci Writing. Next max on Lit is probably best, both for Libraries and because the AI shuns it (likely to be a monopoly). In any case, the key moment is when Map-making is first learned. If you have been doing your job, you should have a better WM than that civ. Leverage this and everything else you have into getting the tech and everyone's map. Then trade around for everything.
In Conquests, it's even more certain when you start with Alpha. Once you have Writing, research Philo next (maxsci all the way; minimum is not attractive in C3C). You'll get it nearly every time. Use it to grab a monopoly tech. With two monopolies, you should be able get all the techs you need. If you've had a good start, you can try the Republic slingshot instead of going to Philo directly. It is quite doable on deity. Trade away CoL after a few turns of Philo.
If all else fails, go bash some heads.