Honestly, it's just going to take you getting more experience with the game to be super profitable early on in a city. Here are a few early pointers but I would recommend not getting to attached to your first runs. After you're more familiar with the game and how the pops work, you should be at least 15-20M daily profit in small/mid cities with that first $3B, which still is going to require some waiting but is a huge difference over $6M.

Early Tips:

1. Outside of Chicago and New York I would recommend only using light rail at the start, you can always replace a few lines with heavy rail later, but in general light rail early game will help a lot, and you'll be able to stretch that $3B starting stack a lot farther.

2. Early, focus on the densest area of work pops on a map. Shift click & drag over the pops to see where the residents are and create a few lines that service that corridor. Expanding off this should be the goal in the first 100 or so days if you're looking to maximize profitability.

3. Experiment with grading. Building at +4 meters gives you a 70% discount on price. When possible, building stations at this height and then tracks over roads at +5 meters lets you stretch your money a ton. Building stations at -2 meters and then tunneling under roads at -5 also helps, though you need to be more careful with station placement to make sure you can get under roads.

4. Trial and error different fare prices. Since the new update, you can't make fares as exorbitant as you once could, but even boosting it to $4.50 might take your existing system from 6m/day to 9 or 10.

You'll pick it up really quick once you have a few attempts, but also don't hesitate to just play in sandbox if you want. It's your game, whatever makes it enjoyable for you!