The role of spin-phonon interaction in affecting the magnetic behavior of two-dimensional ferromagnets remains an open issue. We investigate ultrafast magnetization dynamics in two-dimensional ferromagnetic Fe3GaTe2 at room temperature by employing time-resolved magneto-optical Kerr effect and reflectivity spectroscopy. A two-step demagnetization process is observed. By utilizing a generalized temperature model in conjunction with first-principles electron-phonon coupling calculations, we present a self-consistent phenomenological framework demonstrating that the fast demagnetization stage (<1 ps) and the subsequent slower stage are respectively governed by energy relaxation into distinct high-frequency and low-frequency phonon baths. Compared to 0.05 T applied magnetic field, a stronger magnetic field of 0.4 T accelerates both processes, decreasing the time constants from 0.8 to 0.5 ps (fast component) and from 24 to 20 ps (slow component). The magnetic field accelerates both processes by enhancing spin-flip scattering via modulated different phonon-spin coupling. Moreover, magnetization recovery shortens by 65% (1760 to 620 ps) with magnetic field, attributed to domain wall motion and thermal diffusion. Theoretical analysis and dynamic simulations confirm that these transient behaviors originate from the Elliott-Yafet phonon-assisted spin-flip mechanism. Our findings elucidate microscopic spin-energy transfer mechanisms in 2D magnets and advance prospects for ultrafast spintronic devices.