How can electron move between two metals without the presence of electric field?
The wording of the question hides the answer.

Electrons do not move from Zn to Cu. They move from neutral zinc to cupric ion Cu++. The field arises from the mix of H2O, H+, OH-, SO4--, and Cu++ all around the Zn rod. Could electrons be forced onto Zn from OH- or SO4-- ? No.There is no gain in stability; energy would be needed. Or could electrons be attracted to H+; yes, and even more so to Cu++. And the final products (Zn++ and neutral Cu) would be more stable.