In a world of hardening borders, nations may deprive themselves of enjoying the benefits of cooperative immigrants. Here we analyze the effect of efficient cooperative immigrants on a population playing public goods games. We considered a population structured on a square lattice with individuals playing public goods games with their neighbors. The demographics are determined by stochastic birth, death, and migration. The strategies spread through imitation dynamics. Our model shows that cooperation among natives can emerge due to social contagion of good role-model agents that can provide better quality public goods. Only a small fraction of efficient cooperators, among immigrants, is enough to trigger cooperation across the native population. We see that native cooperation achieves its peak at moderate values of immigration rate. Such efficient immigrant cooperators act as nucleation centers for the growth of cooperative clusters, which eventually dominate defection.