I have started running D&D 5e just now, so I do not have an encyclopedic knowledge of character creation options. We played a first session, with half character generation and half low-key play.
One player made a tiefling warlock and said they use their augury ability that they have since they are a tiefling. I did not carefully go through their character sheets; players are responsible for that, but I also checked some obvious sources and only found that tieflings get thaumaturgy from their race, not augury. But maybe there is some variant that gets augury, or gets to add augury to their spell list, etc. The character is first level.
The player claimed to know the rules but made false claims about them during the session. The player is a stranger to me and the other players. I will, for sure, ask them to show their work at the beginning of the next session, but I would also like to know what the rules actually say.
Is it possible for a warlock tiefling to have access to the augury spell, as a first level character?
I am most interested in official published (not Unearthed Arcana) WotC material, but if there is notable UA or well-known third party material that allows this, that would also be useful information.
(I do not, at the moment, need advice on handling the social situation, and will ask a separate question if it becomes relevant.)