White holes are time-reversed black holes. For a black hole, a particle may fall in with a trajectory that terminates at the singularity. The time-reversed version of that picture is that a particle "is created at the singularity with sufficient speed that it can escape" (roughly).
What causes the creation of such a particle with such "speed"? General relativityEstablished physical theories can't explain this any more than itthey can explain what happens when a particle hits the singularity of a black hole. So in this respect, the answer is "we don't know".
But I also want to emphasize that white holes are gravitationally attractive. Time-reversed gravity still acts in the same direction (imagine the time reversal of jumping into the air and landing). An outflowing particle is slowed as it escapes the white hole's gravitational pull.
(Note that I'm speaking solely of "white hole" solely as a solution to the equations of general relativity. There is no reason to think that white holes can or do exist in the universe.)