In this work, we test the established hypothesis that lunar regolith depth increases with time because the surface is continually exposed to meteorite bombardment. If this hypothesis is correct, younger surfaces should have thinner regolith than older surfaces. Because many of the regolith depth studies in the literature are for surfaces older than 3 Gy, in this paper, we study Mare regions with a wide range of ages between 1.33 Gy and 3.88 Gy. To measure regolith depths, we used the small crater morphology method based on the work by Oberbeck & Quaide. We found median regolith depths between 1.6 m to 4.0 m across our study sites. Importantly, we did not find any correlation between the thickness of the regolith and the age of the surface within the Mare units we studied. We conclude by discussing whether this result represents a true lack of correlation, which would imply an incomplete understanding of regolith formation.