In a galvanic cell,do charges accumulate on electrodes 1st (then redox occur) which produce E in the wire when we connect between electrodes? We study that when we connect a wire between the terminals of a battery ,an electric field in established between terminals  due to potential difference .Is the potential difference result of accumulated charges on terminals. In other words   when an electrode is put in the solution like Zn in ZnSO4  will Zn electrode will become -vely charged ? If not then how does electric field established into wire at exact moment when we connect wire between terminals (electrodes) which essential for electric current .
You can imagine the cell electrodes as capacitors, that are charged by chemical way. 

But the capacitance of these capacitors 

$$C=\frac {\mathrm{d}q}{\mathrm{d}E}$$ 

is very small, so does the accumulated charge $q$.

The charge loses due pushing electrons  through the wires of a closed circuit are balanced by simultaneous recharging by ongoing redox reactions. 

If we consider the zinc electrode of the Daniell cell, the reaction :

$$\ce{ Zn -&gt; Zn^2+ + 2 e-}$$

is charging the electrode negatively, while the opposite reaction:

$$\ce{  Zn^2+ + 2 e- -&gt; Zn}$$

is charging the electrode positively.

The electrode gains such a potential, where both reactions are ongoing at the same rate.