By the time I get to the door is a reference to an expectation of something happening at a future time. He could not yet know the friend is there. But you could say
By the time I got to the door, my friend was already there.
This marks by the time as the time when he is at the door, not a time while going to the door.
As for already there, this is a completed action, so it should also be past tense.
You could say
By the time I get to the restaurant I will be hungry.
as this indicates a future expectation based on a point in time (at the restaurant).
Though it doesn't make great sense, you could say
By the time I get to the door, my friend will be hungry.