I would like to play this game without starting in the ancient era, but I can't find any tips how to play games starting from e.g. a modern or future era (going for EQM in the far future). Are there any general ways into playing these late era games?
In fact even better to start a discussion about all era's but ancient.
Well, later era starts don't get played as often, so there's really not a definitive strategy laid out for each era. What I will say is that with each later era the AI tends to get nerfed a bit, i.e., they don't adjust to things as well and it is easier for the human to take advantage of it. With the real late era...say...Renaissance and above...my one advice is the the Serfdom civic actually has value initially. Allows you to get get up improvements asap since you have access to all the techs first thing. So do mass civic switch first thing - depending on era and what you have access, but run Serfdom first thing. Chop a couple more workers or so out first thing and then get your empire improved asap. Then probably setup to take out an AI quickly nearby.
Also, note that settlers get quite a bit more expensive with each era. Probably wait to get up a strong production base and infra before building, but also makes taking cities quick more valuable.
In other words, your first focus is on your core three cities and worker management to take advantage of their size and free infra.
On modern and higher, you will have access to corps initially I believe, so running Caste early may be good to get quick great people for corps, if corp is the right way to go. Your cities though start with infra like forges so a GE should be easy to get, especially Lizzy for Mining. I forget if you have free markets. Ofc, you can't go wrong with State Prop either. But for Time game, corp is generally the way to go to max score, and Archi should be very good for Sushi. Keep in mind that AIs are likely to start corps as well in this era, so it is a bit of a race to the corps. Lizzy probably best here. Vicky good too though for the IMP trait has some value on settler cost. I forget but I think settlers are like 200h or more.
The one thing you don't get is research buildings, so tech will be very slow until you establish the research modifiers and stuff. That will likely be a priority. But the AIs will be slow to research for a while too. You will be fighting at par military for some time, but can take advantage of numbers while AI still developing.
Lastly, each era gives you more free stuff and starting tech base, dependent on era. Classical starts are the most bare bones..you don't get much. Medieval I think is where you get a second settler, and then Ren and above you get 3 settlers.
Bottom line is that I'd say the human advantage goes up with each era, if you know what you are doing. An early rush or two on neighbors is recommended with the best units/siege of the era.