Data Assimilation (DA) reconstructs the state of a spatio‑temporal system by merging sensor observations with numerical model outputs. Model states are high‑dimensional while observations cover only a tiny fraction of the domain, making DA a large‑scale estimation challenge central to weather forecasting and oceanography. Classical variational methods such as 3D‑Var rely on a hand‑crafted background error covariance that assumes unbiased errors, thus failing to capture state‑dependent correlations or systematic model biases, and their computational cost grows with domain size.\n\nDeep learning (DL) approaches can perform DA and bias correction (BC) non‑linearly, but they usually lack interpretability and provide no calibrated uncertainty estimates. We propose a hybrid framework that couples a convolutional neural network (CNN) with a learnable‑kernel Gaussian Process (GP) to jointly conduct DA and BC from extremely sparse observations. The model is trained end‑to‑end by maximizing the marginal log‑likelihood, learns a data‑driven covariance over the whole grid, and inherently yields the Maximum A Posteriori (MAP) analysis together with its uncertainty.\n\nA patch‑based strategy reduces the $O(N^3)$ training cost of exact GPs over $N$ grid points to $O(N)$ for a fixed patch size. Inference remains exact and only requires solving a linear system whose cost is $O(m^3)$, where the number of observations $m\ll N$, independent of the domain size. The learned covariance can also replace the hand‑crafted one in 3D‑Var, improving accuracy without altering the variational formulation.\n\nExperiments on sea surface temperature and salinity, using both synthetic and real extremely sparse in‑situ observations, show that the proposed framework outperforms 3D‑Var, a classical GP and a competing DL model, while reducing inference time by more than 98% compared to 3D‑Var.\n\nReview: The approach balances physical interpretability with computational efficiency and calibrated uncertainty, making it well‑suited for domains such as oceanography where observations are extremely sparse.