Global measurements of ocean pCO2 are critical to monitor and understand changes in the global carbon cycle. However, pCO2 observations remain sparse as they are mostly collected on opportunistic ship tracks. Several approaches, especially based on machine learning, have been used to upscale and extrapolate sparse point data to dense global estimates based on globally available input features. However, those estimates tend to exhibit spatially heterogeneous performance. As a result, we propose a physics-informed transfer learning workflow to generate dense pCO2 estimates. The model is initially trained on synthetic Earth system model data, and then adjusted (using transfer learning) to the actual sparse SOCAT observational data, thus leveraging both the spatial and temporal correlation pre-learned on physically-informed Earth system ensembles. Compared to the benchmark upscaling of SOCAT point-wise data on baseline models, our transfer learning methodology shows a major improvement of up to 30-52%. Our strategy thus presents a new monthly global pCO2 estimates that spans for 35 years between 1982 and 2017.