Fatigue crack growth is one of the most common types of deterioration in metal structures with significant implications on their reliability. Recent advances in Structural Health Monitoring (SHM) have motivated the use of structural response data to predict future crack growth under uncertainty, in order to enable a transition towards predictive maintenance. Accurately representing different sources of uncertainty in stochastic crack growth (SCG) processes is a non-trivial task. The present work builds on previous research on physics-based SCG modeling under both material and load-related uncertainty. The aim here is to construct computationally efficient, probabilistic surrogate models for SCG processes that successfully encode these different sources of uncertainty. An approach inspired by latent variable modeling is employed that utilizes Gaussian Process (GP) regression models to enable the surrogates to be used to generate prior distributions for different Bayesian SHM tasks as the application of interest. Implementation is carried out in a numerical setting and model performance is assessed for two fundamental crack SHM problems; namely crack length monitoring (damage quantification) and crack growth monitoring (damage prognosis).