Unless you purchase ships from the C-Store / Exchange, open lock boxes, or wait for events that rewards ships / admiralty cards, then you can only get one time use cards from the admiralty system itself as a reward for certain types of missions.
Note that you can also purchase T1 - T5 ships using dilithium from the ship vendor. These are the ships you get to choose from when you level up. The ship vendor also sells a shuttle craft for each faction for something like 32,500 EC.
There are also missions that grant 1x time use ships. (It's one of the reward times other than colonists, prisoners, dilithium, EC and crafting materials). They are obviously not permanent, but you can get a lot of them, including doubles and triples and what not.
In addition, make sure you have all the shuttles your faction has, especially the 25 % maintenance reduction ones greatly help get more out of a smaller supply of ships.
Star Trek Online Advancement: You start with lowbie gear, you end with Lobi gear.
Answers
Note that you can also purchase T1 - T5 ships using dilithium from the ship vendor. These are the ships you get to choose from when you level up. The ship vendor also sells a shuttle craft for each faction for something like 32,500 EC.
In addition, make sure you have all the shuttles your faction has, especially the 25 % maintenance reduction ones greatly help get more out of a smaller supply of ships.