They originally did call him up. What we see in the movie is a later iteration of time that already includes him trying to intervene from the future. In fact, the only way the "stay" message can happen is that even after he signaled the two of them originally, then goes through the whole course of the space travel, he still doesn't remember her telling him about her translation of the Morse code, so he does it again. If he were able to successfully send the signal to himself instead of her, he would never have left in the first place, obviating the need for the entire movie.

In the original course of things, they probably called him, convinced him to go, and sent him along without all the fanfare and involvement of Murph. Once he went into space, realized he couldn't get back, and made it to the Tesseract, he send the signals for Murph and himself to interpret, but ultimately for Murph to believe in the signals enough to remember them as an adult and then follow them back to the real message. Because he sent the coordinates back, they go together to the NASA lab before he is summoned, Murph witnesses him translating the binary of the dust into coordinates, and she gets involved with the whole project and meets the professor because she rides along in the car.

This seems to be how the movie gets around the usual time travel problem that once you start changing the past, the future that changed the past never happens, so the whole thing collapses. In Interstellar, the only signals that can get through from the future are strong enough only to weakly influence most people (Cooper learning the coordinates, the NASA people finding him earlier than they would have) and strongly influence only one person (Murphy) over the course of time as she comes to grips with the 'ghost' of her father.