We report on measurements of the sound velocity and attenuation in a single crystal of the candidate quantum-spin-ice material Yb2Ti2O7 as a function of temperature and magnetic field. The acoustic modes couple to the spins magnetoelastically and, hence, carry information about the spin correlations that sheds light on the intricate magnetic phase diagram of Yb2Ti2O7 and the nature of spin dynamics in the material. Particularly, we find a pronounced thermal hysteresis in the acoustic data with a concomitant peak in the specific heat indicating a possible first-order phase transition at about 0.17 K. At low temperatures, the acoustic response to magnetic field saturates hinting at the development of magnetic order. The experimental data are consistent with a first-order phase transition from a cooperative paramagnet to a ferromagnet below T≈0.17 K, as shown by fitting the data with a phenomenological mean-field theory.