I am going to be playing for the first time and was wondering, are goliaths playable in Adventurers League?
Yes, as long as you abide by the "+1 rule."
The DDAL Player's guide "Character Creation" section says, in part:
All of the races and classes presented in the Player's Handbook plus one other resource from those listed below are available to build your character. (p.2, emphasis in the original)
Pertinent to you, both the Elemental Evil Player's Companion and Volo's Guide to Monsters are listed; those're where you can find goliath to play.
So you can choose to grab a goliath from either of those sources. Note, however, that locks out the possibility of using any character options from Sword Coast Adventurer's Guide or Xanathar's Guide to Everything, for instance.