How is this possible?
If Cooper didn't receive the coordinates he would never go to NASA and he would't have been on the mission. Then would be no one to send the coordinates back in time.
Am I missing something?
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As Dean F. says, this is a common science fiction trope, that you can use time travel to interact with yourself in the past.
However Intersteller attempts to base its story on an fictional extrapolation of current understanding of time, relativity, wormholes and black holes.
So your question has two parts really:
Kip Thorne, a one-time professor of theoretical physics, was a scientific advisor on the movie and he wrote a book about some of the science in it. I would advise you to read this if you really want to get into the detail of this.
Kip Thorne has written scientific papers discussing the theory of 'closed time-like curves', that may be caused by Wormholes. The tesseract (bookcase space) that Coop uses to interact with Murph's room, is a fictional extrapolation of these theories. The premise is that beings descended from humanity are sufficiently advanced to create the tesseract and use the Wormhole to allow Coop to interact with the past.
The question of the paradox has also been considered by physicists, including Kip Thorne. The idea is expressed in the Novikov Self Consistency Principle which posulates for these closed timelike curves, the probability of an event that would cause a paradox is zero
Interpreted in human terms, time is self-consistent, which would mean Coop has no actual self-will here. He found the coordinates in the dust, it is therefore certain that he will create them.
Cooper went back in time and sent the coordinates to himself. It is a time loop where the person involved created his own future by interacting with himself in the past (with help).
The same happens in many time travel stories and movies. Sometimes, the future person is even self-aware enough of the fact that they have to do a certain activity while traveling in the past in order to make the present happen the way they remember it, that they go out of their way to make sure their past self is properly affected by their actions.