What is a trivial $G$-bundle exactly?

Question

Let a fiber bundle be given by a structure $(E,B,\pi, F)$. It is a G-bundle if it is equipped with a maximal $G$-Atlas, i.e. a set of local trivialization charts such that transition maps on their intersections are continuous (wiki definition of $G$-Atlas). What does it mean exactly for it to be trivial? Surely, there must exist a trivialization chart of the whole base space $(B, \phi_i)$, but I'm not sure that every $G$-Atlas must contain such a chart. Is it included in the definition that an atlas of a trivial $G$-bundle includes such a chart? Or can we perhaps prove that every maximal $G$-Atlas includes a base space trivialization chart if it is known that the projection $\pi$ is trivial (i.e. that a base space trivialization chart is possible)? If so, I'd like to know how to prove it.