Early-age shrinkage of concrete can initiate pre-mature cracking, which can compromise the durability of concrete structures. Monitoring capillary pressure, the leading cause of concrete shrinkage, and understanding its evolution is crucial for the performance-based design of concrete, particularly at early-stages when it is more prone to cracking. This study deploys an innovative multi-scale experimental program using high-capacity tensiometers to monitor the capillary pressure up to 2000 kPa. This allowed investigating the effects of key design parameters, including the water-to-cement ratio, GGBS, SRA, and measurement depth, on the capillary pressure evolution in concrete. A new robust deep neural network model was developed to conduct extensive numerical experiments to predict the capillary pressure evolution of diverse mixtures. The net effect of multi-parameters on the capillary pressure can be investigated with this model, providing insights into the optimum design of more durable concrete mixtures with the lowest capillary pressure evolution, and guiding the implementation of appropriate cost-effective shrinkage-mitigating strategies.