  We investigate the early coarsening dynamics of an atomic Bose gas quenched
into a superfluid phase. Using a two-step quench protocol, we effectively
control the cooling rates, $r_1$ and $r_2$, during and after passing through
the critical region, respectively, and measure the number of quantum vortices
spontaneously created in the system. The latter cooling rate $r_2$ regulates
the temperature during the condensate growth, consequently controlling the
early coarsening dynamics in the defect formation. We find that the defect
number shows a scaling behavior with $r_2$ regardless of the initial cooling
rate $r_1$, indicating universal coarsening dynamics in the early stage of
condensate growth. Our results demonstrate that early coarsening not only
reduces the defect density but also affects its scaling with the quench rate,
which is beyond the Kibble-Zurek mechanism.
