  We investigate the interwoven dynamic evolutions of neutral nitrogen
molecules together with nitrogen ions created through transient tunnel
ionization in an intense laser field. By treating the molecules as open quantum
systems, it is found that considering real-time injection of ions and strong
couplings among their electronic states, nitrogen molecular ions are primarily
populated in the electronically excited states, rather than staying in the
ground state as predicted by the well-known tunneling theory. The unexpected
result is attributed to sub-cycle switch-on of time-dependent polarization by
transient ionization and dynamic Stark shift mediated near-resonant multiphoton
transitions. Their combined contribution also causes that the vibrational
distribution of N$_2^+$ does not comply with Franck-Condon principle. These
findings corroborate the mechanism of nitrogen molecular ion lasing and are
likely to be universal. The present work opens a new route to explore the
important role of transient ionization injection in strong-field induced
non-equilibrium dynamics.
