It's extremely difficult to keep up with a deity AI in tech at the start of the game. Deity AI's need fewer beakers to research a tech than you do, and they start with 2 settlers, and pop out more faster.
It's pretty disorienting to be so far behind - it gets worse. Maybe you build up 20 or 30 gold, to create an embassy - it's likely to get demanded from a nearby AI.
Of course, the AI gets out of despotism faster than you do, which just makes it worse.
That said.... you can overcome that. Find out what techs the AI won't generally research first and get those - writing, literature, math, currency - and use those in trade. Buy techs like horseback riding after everyone else has researched them and the cost is lower. Trade for techs that a couple of AI don't have, so you can use it for techs they have that you don't.
Keep growing, as fast as you can.
Pointy stick research - war on the nearest neighbor, take a few towns and beat up a bunch of their units and make peace for techs. Do the same for the next AI over.
Another strategy is to be scientific and not have other scientific civs. Your free tech will help you and the cheaper libraries will help a lot.