You don't draw cards - you select them.
Before the mission you select a number of cards equal to your hand size.
For your very first mission use all your level 1 cards.
After the first mission, add the "X" cards to your available card pool. When starting a mission, select a number of cards equal to your character's hand size from the available pool. When you level up, you add one card to your pool, but you may still only select a number of cards equal to your hand size for each scenario.
The rulebook page 12 wrote:
Next, players should decide which ability cards they would like to put in their hand, choosing from the pool of those available to them. A player must select a number of cards equal to his or her character’s hand size. When first starting the game, a player’s hand should only consist of the set of Level 1 ability cards for the character’s class. Once a player has become familiar with the class, he or she can begin substituting out Level 1 cards for the more complex cards with X as the level. Once the character begins to level up, he or she will also get access to higher level cards to add to his or her hand by pulling others out.
When you have selected your cards for the scenario, you start with all of them in your hand.