The evidence for short-lived radioisotopes in chondritic meteorites requires that no more than about a million years elapsed between nucleosynthesis of the isotopes and the formation of cm-sized solids in the solar nebula. We show that this abbreviated time scale can be best accommodated in a scenario where an interstellar shock wave transports the isotopes from the parent star to the presolar cloud, triggers the collapse of the presolar cloud, and injects a significant fraction of its dust grains into the presolar cloud. Shock waves from both distant supernovae and from evolved red giant (AGE) stars appear to have sufficient momentum to trigger collapse of a solar-mass cloud. In addition to momentum-induced collapse, the high temperature regions further behind supernova shock fronts and planetary nebulae shells are also able to crush a presolar cloud into collapsing. Both supernovae and AGE star shock waves are able to inject about 10% to 20% of their incident dust grains into the collapsing presolar cloud.