Possible? Yes. Easy? Not really. Easy to start, be, and permanently remain a freelancer? Not so much.
Your starting credits won't get you far, and you don't have a lot of options on the planet you start on. You can save CPs to get yourself a basic ship, and then get started.
A better option is to join a faction, at least in the short term, and earn a paycheck for a few months. Then you can use that money to play the trading game to supplement your income (or even replace it if you want to quit the faction at that point), and they'll probably also give you the use of a ship, which will give you mobility until you have enough to buy your own.
____________"May the Grace of Ara go with you, and His Vengeance be wrought upon your enemies."
Only fools and children dream of heroes.