World line coordinate finiteness
Particles are generated and destroyed all the time. This is obvious for photons, but also holds for massive particles. Today most particles are stable and long-living, but shortly after the big bang the universe was so hot that particle generation and destruction were in some equlibrium and all particles participated in this process (for photons this continued until the epoch of re-ionisation at redshift $z\sim1000$. There is definitely no particle around today that existed all the time since $t=0$.