You can choose exotic languages at character creation
At first glance this question seems pretty straight forward:
Humans typically learn the languages of other peoples they deal with, including obscure dialects. SRD p. 5
The use of the word obscure would seem to imply to me that an exotic language is a legitimate starting pick.
But wait, there's a complication..
Talking about langauges more generally, the SRD says:
‘Choose your languages from the Standard Languages table, or choose one that is common in your campaign. With your GM’s permission, you can instead choose a language from the Exotic Languages table’. SRD p. 59
GM permission? Could there be some restrictions, after all?
So do you need permission in order to create an Adventurers League character with an exotic langauge? No.
This quote from the DDAL FAQ (on page 4), in a question specifically about selecting languages at character creation, seems to clear up any uncertainty:
Characters may choose exotic languages from any allowed rules source, even if that rules source wasn’t used to create that character (i.e., a character created using the PHB and VGM may still choose a language from the SCAG).
Great news for lovers of exotic languages.
P.S. Following discussion in the comments:
This might not be RAW guidance as explicit as finding a text saying...
'Exotic languages are allowed to be chosen, as racially gained languages, during AL chracter creation'
..but in the absence of a RAW argument that exotic languages should be prohibited, it makes sense, following the reasoning in my answer, to consider it Rules as Intended that exotic languages are allowed as racial picks.