What you experience is totally normal imo. If you start without a Goldmine or similar, you'll always fall behind. You need to improve your tech-trading skills, so you get 5 techs for your 1, and you need to make use of bulbs, to get techs which can be traded to lots of civs.
There are imo two approaches early on:
1. The Alpha beeline
This is the superior approach but requires you to be good at fogbusting and doing with Warriors only, because you'll skip BW in many cases and sometimes will even go TW Pottery instead of AH. If you're first or second to Alpha, it's almost impossible to not be able to compare with the AIs if you play well.
2. The Asthetics approach
This approach gives you more freedom. You can research more basic techs, and it's unlikely that AI will go for Aesthetics, so you'll definitely get good tradegood, for which you can get Alpha and Maths. You'll fall far behind with this approach, but you'll be able to catch up again, though it's difficult.
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There is a 3rd approach, which is the HBR + Maths approach, but I never had success with that one. Getting Alpha is easy but HAs are too weak for my taste, I have much more success with Elepult. In this approach you beeline HBR after Writing, and follow up with Maths and try to get Alpha for both. Sometimes, you can even trade HBR for IW and get Alpha without Maths.
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Regarding expansion: I often write, that I delay the 2nd Worker as much as possible. I build up to 5 Settlers before building a 2nd Worker. I improve 3-4 tiles at the capital, then I hop over to the next city with my Worker, improve 2-3 tiles, next city and so on. On Deity, it's more important to grab land first, and working unimproved tiles also isn't really that bad in the beginning, also cities are small, so doing with only very few improvements (and ofc. no roads) is possible.
For Elepult, 4 cities is a good number, for HAs 3 is good, for Cuirrassiers, try with 6 or 7. Less is possible, but then it gets tough. I've already won with Cuirrassier breakouts from 3 cities, 1 having no food, but those games require precision work at the wars, like weakening a target and isolating it while building the perfect stack and don't lose more battles than the RNG shows.
Regarding the economical crash, read my guide on hybrid economy, there are lots of tricks to get

, like i. e. whipping a Warrior when he's almost complete and chopping heavily into it on top. If you have foreign TRs, you at least shouldn't go bankrupt, and with tricks like the one with the Warrior, you can always make it to Currency.