Fly a large plane(>200 pax) 3000-3700NM with 1x daily flight(typically these are transatlantic routes). You only have to pay for 1 Slot each day.
Paying for slots has nothing to do with it.
It boils down to primarily 1 of 2 things:
1> Fly a large plane on a long-distance, high-margin (usually through a high First/Business configuration, though that's been nerfed a bit, so you can't fly 100% premium immediately) international flight. This generates high-profits which allows quick huge loans which you use to buy lots more planes, rinse and repeat.
2> Fly a large plane on the shortest, highest-density routes you can find. This gives you huge margins as well. If you can turn a single large plane 4 or 5 times per day, you'll make money hand-over-first, and again you buy lots of planes, put those on similar routes, and keep repeating.
One of the biggest mistakes people make is trying to 'stake claims' on routes. Rather than filling up the absolute biggest routes first, they create flights all over. This increases your costs in a very big way. The other big mistake is flying to "big name" cities first even if they're a lot further away. New York to Los Angeles is a great route -- but while you're busy flying there once per day, your competitor is flying to Detroit 3 times per day with the same single plane and making twice the profits.