I want to install a deadbolt into the garage door but with that one beam of wood I feel someone could easily kick it open?
I would sister up another 2x4 inside of the existing stud (weird to see a single stud there anyway, usually you would have a stud and a trimmer). Secure it with screws along the entire length.
Use heavy bolts with washers from the opening/door side to the back side of the studs, above and below the strike plate/latch area. To make them sit flush on the opening/door side, countersink the heads.
Then install a heavy duty reinforced strike cup and plate unit, there are many types and sizes available:
I had a similar situation many years ago in an apartment where the door was kicked in. I cut out a section of the 2x4 jamb and replaced it with hard maple and a piece of bar stock. That is great for the jamb, but, like others have pointed out, the deadbolt itself and the door are no stronger.