Today the Sun is very far from other stars, but early in star formation (within nebula) the stars are
1. much closer together
2. have a higher rate of material ejection (mass exchange)
3. likely have more benign radiation environments unless near a star, due to GCR shielding by nebula gas
4. likely have higher equilibrium temperature in interstellar/interplanetary space
Combined, these factors yield orders of magnitude improvement in panspermia efficiency vs the Sun.