If a zinc plate is dipped into pure water, maybe one zinc atom produces a $\ce{Zn^{2+}}$ ion while the two corresponding electrons are staying back in the metal. But his is only valid for the first zinc atom. When the second zinc atom will do the same, it is prevented by the presence of one positive $\ce{Zn^{2+}}$ in water and the negative charges in the metal. So the second zinc atom will not be ionized and dissolved. The concentration of zinc ions in solution is then of the order of $\pu{10^{-23}}$ mole per liter. This is totally negligible. But it is sufficient to prevent further ionization of zinc atoms plus dissolution of the corresponding $\ce{Zn^{2+}}$ ions in the future.

If a zinc plate is dipped into pure water, maybe a small number of zinc atoms produce $\ce{Zn^{2+}}$ ions while the corresponding electrons are staying back in the metal. But this is only valid for the first few zinc atoms. When additional zinc atoms will do the same, they are prevented by the presence of positive $\ce{Zn^{2+}}$ in water and the negative charges in the metal. So additional zinc atoms will not be ionized and dissolved. So few ions are generated that the concentration of zinc ions in solution is totally negligible. But it is sufficient to prevent further ionization of zinc atoms plus dissolution of the corresponding $\ce{Zn^{2+}}$ ions in the future.