Hi!
This was possible in Sid Meiers Pirates (the main inspiration, obviously) but it lead to a player having a large frigate (the second best ship in the entire game) 10 min after starting a new game. I didnt like that as you lost one main driver/goal in the game (to get a nicer ship).
If you have any ideas on how aquiring ships can be made more fun (but still hard) please let me know! Otherwise accumulating wealth and then buy a ship seems pretty good for me (it also makes gold more useful, it was pretty pointless in "Pirates!" except for buying pices of maps and other trinkets)