The part of this park near the west side is quite noisy from the road, but once you go deeper in, you can't hear it anymore.

Literal

This park [possessive-の] west-side [to-に] close place [topic-は], road [possessive-の] noise [also-も] loud but, interior [to-に] enter [conditional-と] already can't-hear.

Uses ~と as an automatic conditional — when you enter the interior, the noise naturally disappears. The spatial contrast between 西側に近いところ (near the west side) and 奥に入ると (going deeper in) structures the whole sentence. もう with the negative 聞こえない means 'can no longer hear.'