so what are they doing, to be so much better than me, at begin ?... My build order is 2 scouts, 1 slinger ( for eureka of bowman ), 1 warri, 1 builder, and then it depends a little bit, if I have 50% faster melee and ranged units, I build some of them( 3,4 units more ).Or if need, a monument, a 2nd builder or when having 50%settler prod speed settlers.
Few turns before the first better goverments types are coming I finish the goverment district. I take then the 50% fast settler speed and free worker when founding a city. And then many many many settlers. And as germany my goal is to tech Apprenticeship and then replacing the 50% settler speed for 20% discount on buying tiles. With Hansa and the 100% more district bonus for industrial neighbours I can outproduce any other player. Then there is also enough production left for wonders. Some times I go for Stonehange at begin.
TLDR : you are waiting much too long to expand.
You should probably build your first settler before waiting for the card. It's quite common for me to go unit -> settler if I have good tiles, or unit -> builder -> settler otherwise.
reaching 6 pop for early empire inspiration often come earlier if you actually produce at least one settler without it.
Stonehenge from the start is a huge investment, it's usually not worth it unless your whole game plan revolves around getting first pick on a religion. Even as China, it's hard to land it without sacrificing your growth. Wonders are always a huge trade off, early wonders even more so.
For a better success, the first phase of the game should be focused on expansion expansion expansion. You might slot in a quick district (if it takes more than 6 turns,, probably best to skip it) for inspiration, or a few units to explore/defend as necessary, but really everything should serve your expansion and it should take priority every time it's possible. Try to produce your settlers at the same time to get maximum benefit from colonization, and your builders when you're running Ilkum (once you got the cards).
Best recommendation I can give you : play a few starts to T50 and see how many cities you can get in that amount of time, trying to maximize it with as little consideration for anything else as you can. I know it's hard for many players, but at least as an exercise, try to play the game as if wonders didn't exist either.
Also, plant your first cities for their immediate benefit, not for their third ring tile potential. Reasonable expectations are : fresh water, at least one 2f/2p tiles in first ring (any tiles with better f/p yields are to be considered great tiles), at least one luxury or bonus resource and at least another 2/21 tile in second ring.
Resource are specially valuable if their improvement is needed to trigger early eurekas your other cities can't provide (if you have a jungle cap with silk and 2 bananas but no wheat/rice, a second city with one of these resources is more valuable as it help you to get the irrigation eureka).
Early cities should be as autonomous as possible, meaning able to produce what they need from first ring tiles plus max 2 to 3 second ring tiles.
There are of course many other skills required, even from a purely "builder" point of view, but training yourself in early expansion will probably be the most beneficial first focus. Just ignore the ancestor's hall benefit and don't hesitate to produce at least one settler before colonization's +50% is available.
Basically early game goals should be : get as many cities as possible, first two after your capital should be strong from the start, get political philosophy as soon as possible.