The Integrated Science Investigation of the Sun instrument suite onboard NASA’s Parker Solar Probe mission continues to measure solar energetic particles and cosmic rays closer to the Sun than ever before. Here, we present the first observations of cosmic rays into 0.1 au (21.5 solar radii), focusing specifically on oxygen from ∼2018.7 to ∼2021.2. Our energy spectra reveal an anomalous cosmic-ray-dominated profile that is comparable to that at 1 au, across multiple solar cycle minima. The galactic cosmic-ray-dominated component is similar to that of the previous solar minimum (Solar Cycle 24/25 compared to 23/24) but elevated compared to the past (Solar Cycle 20/21). The findings are generally consistent with the current trend of unusually weak solar modulation that originated during the previous solar minimum and continues today. We also find a strong radial intensity gradient: 49.4 ± 8.0% au−1 from 0.1 to 0.94 au, for energies of 6.9–27 MeV nuc−1. This value agrees with that measured by Helios nearly 45 yr ago from 0.3 to 1.0 au (48% ± 12% au−1; 9–29 MeV nuc−1) and is larger than predicted by models. The large anomalous cosmic-ray gradients observed close to the Sun by the Parker Solar Probe Integrated Science Investigation of the Sun instrument suite found here suggest that intermediate-scale variations in the magnetic field’s structure strongly influence cosmic-ray drifts, well inside 1 au.