A/the employment agreement

Hello Teachers.

He received a verbal job offer on Monday. An/the employment agreement followed a day later.

I am struggling: "an"? "the"? My teacher says: either is possible.

"An employment agreement" is fine if I conceive of it as a countable document that needs to be introduced for the first time.

"The" is fine if I conceive that there is only one employment agreement or at least only one that can logically flow from the context (every job offer produces an employment agreement).

Either way, she says, I can use either without making a mistake. She prefers "an".

Do you agree with this? I find it strange that it can be both.