"Early running" refers to starting a task or activity before the expected or usual time, typically in the beginning stages or as soon as possible. Full definition
A few days earlier I ran four miles with friends and I was ready to swear off running forever. (rachelheldevans.com)
It happens sometimes that we have a good early run which tails off or we finish strongly. (justarsenal.com)
Those higher energies should allow more and heavier particles to arise than earlier runs saw, potentially revealing exotic particles that finally push the bounds of the standard model. (scientificamerican.com)