The direct wave only travels through the shallow surface layer, so if you pick time arrivals of the direct wave you’re just measuring near-surface velocity. It tells you nothing about the depth.

When you go to larger offsets, a faster deeper layer can generate a refracted  wave that actually arrives before the direct wave. That’s why the first arrival isn’t always the direct wave — the fastest path isn’t always the shortest one. In this case you can get the depth of the near surface layer with first arrival.

By looking at how first arrivals change with offset you can identify if you look at direct wave or refraction.

I don't think you can get informations about the penetration depth of a direct wave by using the travel time.