Here we present a detailed muon spin relaxation (mu SR), neutron diffraction, and ac-susceptibility study of Yb2Sn2O7 that shows that despite the onset of ferromagnetic long-range order at T-c approximate to 0.140 K, the low-temperature phase of this material remains highly disordered with glassy dynamics that span various frequency decades. We suggest that the observed disordered ground state might be made of infinite, percolating clusters coexisting with smaller ones. This mesoscopic cluster glass state would be the result of the enhanced effect of even a small amount of disorder, capable of disrupting the "clean" ordered state near a quantum critical point.