The generation and control of surface acoustic waves (SAWs) in a magnetic material are objects of an intense research effort focused on magnetoelastic properties, with fruitful ramifications in spin-wave-based quantum logic and magnonics. We implement a transient grating setup to optically generate SAWs also seeding coherent spin waves via magnetoelastic coupling in ferromagnetic media. In this work we report on SAW-driven ferromagnetic resonance (FMR) experiments performed on polycrystalline Ni thin films in combination with time-resolved Faraday polarimetry, which allows extraction of the value of the effective magnetization and of the Gilbert damping. The results are in full agreement with measurements on the very same samples from standard FMR. Higher-order effects due to parametric modulation of the magnetization dynamics, such as down-conversion, up-conversion, and frequency mixing, are observed, testifying the high sensitivity of this technique.