AN is an indefinite article. You use indefinite articles when describing something "not specific".
I need an apple. *Not a specific apple, but any apple.
Use AN when talking about a thing which is new, unknown, or introduced to a listener for the first time. Also use AN when you are asking about the existence of something.
Jennifer is an optometrist. Jennifer is being introduced
AN can also be used to introduce what TYPE of thing we are talking about.
This is an excellent movie. Describing the movie
It is important to know that AN can only be used with singular nouns.
THE and THIS are definite articles. They are used to describe something "specific". Use THE/THIS when talking about something which is already known to the listener or which has been previously mentioned, introduced, or discussed.
There is a pencil in my purse. The pencil is yellow.
Thank you for walking the dog.
Unlike AN, THE can be used with both singular and plural nouns. Like AN, THIS can only be used with singular nouns.
While they all 3 do technically work, I would suggest using THE or THIS as it specifically refers to the interview opportunity. If you were asking for an interview, AN would be more appropriate, in my opinion.
Can you get me an interview with your manager?