The first evidence of electroweak (EW) production of pairs of Z bosons in association with two jets (jj) in the final state ZZjj $\to$ $\ell \ell \nu \nu$jj, where $\ell$ = e, $\mu$, is reported by the CMS experiment. The analysis is based on a data sample of proton-proton (pp) collisions at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb${}^{-1}$. Events are selected by requiring exactly two leptons of same flavor and opposite charge, large missing transverse momentum, and two jets with a large rapidity separation and large invariant mass. The EW production cross section in a fiducial volume is ${\sigma }_{EW}$(pp $\to$ ZZjj $\to$ $\ell \ell \nu \nu$jj) = 0.37${}_{-0.12}^{+0.14}$ (stat)${}_{-0.06}^{+0.06}$ (syst) fb, in agreement with the standard model prediction of 0.39 $\pm$ 0.06 fb. The observed (expected) significance of the signal is 3.1 (2.8) standard deviations. Limits on anomalous quartic gauge couplings are derived in terms of dimension-8 effective field theory operators. A combination with the previously reported result from the ZZ decay channel with four charged leptons yields an observed (expected) significance of 5.0 (4.5) standard deviations for the EW production of Z boson pairs.