I'm trying to begin getting into D&D (being taught by a GM friend) and I was thinking of creating a Genasi character. I was wondering if a Genasi could have a humanoid; but not human, lineage as well. Such as an Orc which I believe can interbreed with a Djinn. It would not be for anything besides physical features but I don't want to be uninformed. Thank you ahead of time from a newbie!

You can pretty much do anything your DM is okay with. I don't think the forgotten realms lore specifies genasi require human parentage (I am not fully knowledgeable on official lore though).

The race's description acknowledges that non-human parents are a possibility:

Seen in silhouette, a genasi can usually pass for human. Those of earth or water descent tend to be heavier, while those of air or fire tend to be lighter. A given genasi might have some features reminiscent of the mortal parent (pointed ears from an elf, a stockier frame and thick hair from a dwarf, small hands and feet from a halfling, exceedingly large eyes from a gnome, and so on).