Laser filamentation generated when intense laser pulses propagate in air has been an attractive phenomenon having a variety of potential applications such as detection and spectroscopy of gases at far distant places. It was discovered recently that the filamentation in air induces 'lasing', showing that electronically excited N2(+) is population-inverted, exhibiting marked contrast to the common understanding that molecular ions generated by intense laser fields are prepared mostly in their electronic ground states. Here, to clarify the mechanism of the population inversion, we adopt few-cycle laser pulses, and experimentally demonstrate that the lasing at 391 nm occurs instantaneously after N2(+) is produced. Numerical simulations clarify that the population inversion is realized by the post-ionization couplings among the lowest three electronic states of N2(+). Our results shed light on the controversy over the mechanism of the air lasing, and show that this post-ionization coupling can be a general mechanism of the atmospheric lasing.