Based on 6 months of OBS data from the Cascadia Initiative experiment near the Juan de Fuca Ridge, we obtain Rayleigh wave group and phase speed curves from 6 s to about 20 s period from ambient noise cross correlations among all station pairs. We confirm the hypothesis that the dispersion data can be fit by a simple age-dependent formula, which we invert using a Bayesian Monte Carlo formalism for an age-dependent shear wave speed model of the crust and uppermost mantle between crustal ages of 0.5 and 3.5 Ma. Igneous crustal structure is age invariant with a thickness of 7 km, water depth varies in a prescribed way, and sedimentary thickness and mantle shear wave speeds are found to increase systematically with crustal age. The mantle model possesses a shallow low shear velocity zone (LVZ) with a velocity minimum at about 20 km depth at 0.5 Ma with lithosphere thickening monotonically with age. Minimum mantle shear velocities at young ages are lower than predicted from a half-space conductively cooling model (HSCM) and the lithosphere thickens with age faster than the HSCM, providing evidence for nonconductive cooling in the young lithosphere. The shallow LVZ is consistent with expectations for a largely dehydrated depleted (harzburgite) mantle with a small, retained near-ridge partial melt fraction probably less than 1% with melt extending to a lithospheric age of approximately 1 Ma (i.e., ∼30 km from the ridge).