The success of organic-inorganic perovskites in optoelectronics is dictated by the complex interplay between various underlying microscopic phenomena. The structural dynamics of organic cations and the inorganic sublattice after photoexcitation are hypothesized to have a direct effect on the material properties, thereby affecting the overall device performance. Here, we use ultrafast heterodyne-detected two-dimensional (2D) electronic spectroscopy to reveal impulsively excited vibrational modes of methylammonium (MA) lead iodide perovskite, which drive the structural distortion after photoexcitation. Vibrational analysis of the measured data allows us to monitor the time-evolved librational motion of the MA cation along with the vibrational coherences of the inorganic sublattice. Wavelet analysis of the observed vibrational coherences reveals the coherent generation of the librational motion of the MA cation within ∼300 fs complemented with the coherent evolution of the inorganic skeletal motion. To rationalize this observation, we employed the configuration interaction singles (CIS), which support our experimental observations of the coherent generation of librational motions in the MA cation and highlight the importance of the anharmonic interaction between the MA cation and the inorganic sublattice. Moreover, our advanced theoretical calculations predict the transfer of the photoinduced vibrational coherence from the MA cation to the inorganic sublattice, leading to reorganization of the lattice to form a polaronic state with a long lifetime. Our study uncovers the interplay of the organic cation and inorganic sublattice during formation of the polaron, which may lead to novel design principles for the next generation of perovskite solar cell materials.