After 20 hours of casual gameplay and experimenting with various ways to earn money, I’ve ranked them from worst to best (in my personal opinion):

1) Shooting asteroids,
2) Trading (with travel distances of 20,000-30,000)
3) Completing freelance missions
4) Relying on scavenger swarms on derelicts, selling everything they scavenged

By following these methods, I managed to buy my first ship, a frigate named Abeja, for 2,618,760 credits.
During that time, I was at a high level and saving up to buy the Poseidon Cruiser, priced at 9,662,150 credits.
Unexpectedly, I stumbled upon a much faster way to earn money.

You'll need to be at least level 15 and invest in the 3 perks for the merchant, which improve trading prices by +12%.

1) Save up to 2,500,000 credits.
2) Purchase a license for 50,000 credits, which gives you +5,000 credits per month.
Tip: Licenses can be found at stations when you are allied with that faction.
If you have a positive reputation of +2,500, all licenses can be found at Spire (located one hex down from planet Hogosha).
3) Hire Officer Salley Piper, who can be found at Rayen Freeport (salary: 4,350 credits per month). She provides a +15% bonus to trading prices.
4) Buy a second license for 250,000 credits (e.g., Wasteland stations offer better prices for all goods).
5) Travel to Yxaril Wasteland Depot Station.
6) Purchase the Warlock III light weapon for 2,142,053 credits.
7) Sell that weapon for 2,291,996 credits.
8) Repeat steps 6 and 7 to earn a net profit of 149,943 credits per trade.
9) Once you’ve earned enough money, purchase a second weapon. If there’s no third one available in the store, save your game and reload—this refreshes the store’s inventory.

a) Go to the Systems tab, where you’ll find two sub-tabs: Your Ship and Drydock.
b) In the Your Ship tab, ensure that no weapons are equipped.
c) In the Drydock tab, press Shift + Left Click to buy the weapon.
d) Switch back to the Your Ship tab and press Shift + Left Click to sell the weapon.
e) Scroll down with the mouse wheel to locate the weapon.
f) Repeat steps c to e for fast buying and selling.

By using this method, I was able to quickly buy the Tzar Carrier for 33,244,050 credits, with plenty of extra money to purchase other ships and try them out.

Here is an image with Warlock I, II, and III light weapons and their prices, in case you can't save up to 2,500,000 credits:
Warlock I nets you 28,163 credits.
Warlock II nets you 83,828 credits.
Warlock III nets you 149,943 credits.

Let me know if this works for you!