This paper presents an efficient pipeline for estimating the altitude of an unmanned aerial vehicle (UAV) using a commercial off-the-shelf mm-wave radar. The proposed method leverages a synthetic aperture radar (SAR) algorithm to generate high-resolution depth maps (DMs) of the terrain directly beneath the UAV (nadir). In this work, a depth map (DM) refers to a SAR image reconstructed in the UAV nadir plane. These DMs are fed into a lightweight machine learning (ML) model to accurately estimate the UAV's altitude. To meet the computational and power constraints of UAV platforms, we employ the polar format algorithm (PFA) as a low-complexity SAR processing method. The use of DMs as high-level features enables the deployment of a simple yet effective ML model for altimetry. Additionally, since GPS-based altitudes are referenced relative to a fixed point (e.g., the UAV's take-off location), we derive a nadir depth profile by subtracting GPS altitude from the radar-based estimates. The proposed approach is validated through real-world UAV flight experiments, demonstrating its effectiveness for accurate radarbased altimetry and depth profiling.