I used to play this loads as a kid, but I had clearly forgotten a lot of the strategies for getting out of the early game and into the multi-billion railway empire stage. I have found the tips on this page helpful: https://nylon.net/ttd/starting.htm
Following that, I have now got into the 1980s and have a vast and rather unwieldy network of trains ferrying livestock and goods all over the shop. The game does quite suddenly transition from “struggling to make ends meet” at the start to suddenly money being of no concern. The game at that point just becomes one of maximising profit and trying to make your networks as streamlined as possible. Definitely fun, but very different from the game as it presents itself to on first boot-up, in 1950.
One very important aspect which took me long to figure out: to make a city grow, arrange some inner-city transport. In my first attempts, I would just build a nice station and transport passengers to other cities, and then wonder why the city never became larger. Only with multiple stops, this will happen.
What also helps speeding the process up is building roads for them. Preferably in a chessboard structure. Two-by-two squares for houses, then road again.