More than ten years ago, the observation of the low-energy structure in the photoelectron energy spectrum, regarded as an “ionization surprise,” has overthrown our understanding of strong-field physics. However, the similar low-energy nuclear fragment generation from dissociating molecules upon the photon energy absorption, one of the well-observed phenomena in light-molecule interaction, still lacks an unambiguous mechanism and remains mysterious. Here, we introduce a time-energy-resolved manner using a multicycle near-infrared femtosecond laser pulse to identify the physical origin of the light-induced ultrafast dynamics of molecules. By simultaneously measuring the bond-stretching times and photon numbers involved in the dissociation of H₂⁺ driven by a polarization-skewed laser pulse, we reveal that the low-energy protons (below 0.7 eV) are produced via dipole-transitions at large bond lengths. The observed low-energy protons originate from strong-field dissociation of high vibrational states rather than the low ones of H₂⁺ cation, which is distinct from the well-accepted bond-softening picture. Further numerical simulation of the time-dependent Schrödinger equation unveils that the electronic states are periodically distorted by the strong laser field, and the energy gap between the field-dressed transient electronic states may favor the one- or three-photon transitions at the internuclear distance larger than 5 a.u. The time-dependent scenario and our time-energy-resolved approach presented here can be extended to other molecules to understand the complex ultrafast dynamics.