Other players and factions sell ships. However even the smallest fighter is in the hundreds of thousands of credits range. Also the ship won't be at your location so you'd have to have it delivered.
However, I believe there is a group giving out ships to new players in the Traders Lounge, so maybe look there. If you join a faction (something we suggest strongly) they will generally provide you a ship to use at the beginning and pick you up and take you to that ship.