You could if there had been a President in the past.
Let's imagine that we don't have a president at this moment (and we know that it can be only one)...
Can we say: We never had a meeting with the president?
I would like to know is it possible to use the definite article for a role, title… that is unique, even though we don’t know who that person is or hasn’t been selected yet?
Yes, you can.
After Kennedy was assassinated, it took several hours before Johnson was sworn in. Johnson was acting President instantly, by the Constitution. At that point, it would have been appropriate to say "I will have a meeting with the President tomorrow." And that would have been referring to Johnson.
Let's imagine that we work in a company, and we don't have a boss... And we never did... And it can be only one person.
Can we say:
I've never had a meeting with the boss. I really wouldn't know how to act in that situation.
I see... :)