The persistent spread in model estimates of cloud feedbacks remains a major challenge in climate science. While emergent constraints have offered a path to filter models post-facto, their success has been limited. This work introduces a novel, alternative approach: directly calibrating a climate model with observations to produce constrained projections. We present results from the CliMA atmosphere-land climate model, which features machine learning components and process models for turbulence, clouds, and convection. These components are first pre-trained offline using high-resolution simulations and then calibrated online against global Earth observations. The calibration methodology produces a posterior distribution over the uncertain model parameters, yielding a model that more faithfully reproduces the present climate and its variability. By sampling from this posterior distribution, we generate an ensemble of observationally-calibrated model configurations. We then run climate change experiments with this ensemble to produce new, constrained estimates of cloud feedbacks. This method directly integrates observational uncertainty into the model itself, providing robust, observationally-grounded climate change projections with quantified uncertainty.