Maybe this wikipedia definitions will help:
In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system (such as its volume, pressure and temperature). Entropy expresses the number $Ω$ of different configurations that a system defined by macroscopic variables could assume. Under the assumption that each microstate is equally probable, the entropy $S$ is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant $k_B$. Formally (assuming equiprobable microstates),
In an expanding universe, the number of microstates is continually growing : in the beginning ( lets skip the quantum mechanical inflation time and count entropy after that) the continuous particle exchanges in the quark gluon plasma, the continuous radiation from charged particles inevitably lead to a large increase with time of the number of microstates. There is black body radiation continuously from all masses , after all even now (which is one way of looking at starlight).