Recent experimental observation [Milner and Hutchens, Mech. of Mat., 2021] suggests that crack formation during rapid cavity expansion in low modulus, highly-deformable solids depends on the ratio of the rate of expansion and the acoustoelastic wavespeed, similar to observations in rock and metal [Grady and Kipp, Frac. Mech. of Rock, 1987]. Here, we explore the effect of material non-linearity on predictions of the number of cracks formed at the cavity surface. We find that non-linearity influences crack formation only when the cavity-size normalized elasto-fracture length is greater than one and the cavity's rate of expansion is greater than the acoustoelastic wavespeed. The sensitivity of these predictions on the assumed fracture geometry, either a spherical damaged zone or a discrete cracks, suggests a direction for further experimentation that may illuminate crack formation mechanism in soft solids under dynamic loading.