This is a summary of my experience of earning ~3-4 billion credits to get me enough money to buy a fleet carrier. It is assumed that you already have at least 500-600 million credits and trade-specced Cutter or T9. Here are details on what works as of July 2021 and what is not.
What does not work: Robigo runs. Passengers there are picky, frequently requiring first class cabins (forget about economy). Even in Beluga you get 20-25 millions per run, and you need to be involved. Doing 100+ runs takes ages, and you'll need to actually play the game.
Exploration kinda works, but it takes ages to get good amount of money. If you want, you can circumnavigate the galaxy. See you next year.
Plain old commodity trading. Find a loop trade route on EDDB with both stations within 50ls of their stars and have a good supply. Then just go around, with minimal manual intervention to buy/sell and turn your ship's nose towards the destination. You'll get 15-17 millions per run on a good route. This is faster than Robigo and can be done as background activity. Boring as hell.
Mining probably also works, but takes a lot of time and you also need to actually play the game.
Stacking massacre missions. Works for combat-oriented players.
Trade community goals. Prices are usually very high at dropoff point. You get 15-20 millions in profit per run.
My favorite way. Look for the faction in expansion state. Preferably player faction which has a lot of systems. Get allied with them — drop 5-7 millions of exploration data, donate a few millions or just sell things for profit at their stations. Then go from station to station (controlled by these factions) and look for high-paying missions that require you to source and return valuable commodities (like gold or silver) or mine some minerals (usually gallite or bertrandite). Just be careful not to take missions for mining-only commodities that you can't just buy.
Usually these are wing missions and they require you to provide 700 to 1500 units of required commodity. Then find nearby station with a good supply that sells it (use EDDB) and just do missions, one after another. Profit is usually 35-40 millions per mission. With average luck, you can complete 3-4 missions per hour. Sometimes even more. You will earn billions with little effort and quite fast.
Enjoy you new fleet carrier.