Children's health studies support an association between maternal environmental exposures and children's birth outcomes. A common goal is to identify critical windows of susceptibility--periods during gestation with increased association between maternal exposures and a future outcome. The timing of the critical windows and magnitude of the associations are likely heterogeneous across different levels of individual, family, and neighborhood characteristics. Using an administrative Colorado birth cohort we estimate the individualized relationship between weekly exposures to fine particulate matter (PM$_{2.5}$) during gestation and birth weight. To achieve this goal, we propose a statistical learning method combining distributed lag models and Bayesian additive regression trees to estimate critical windows at the individual level and identify characteristics that induce heterogeneity from a high-dimensional set of potential modifying factors. We find evidence of heterogeneity in the PM$_{2.5}$-birth weight relationship, with some mother-child dyads showing a 3 times larger decrease in birth weight for an IQR increase in exposure (5.9 to 8.5 $μg/m^3$ PM$_{2.5}$) compared to the population average. Specifically, we find increased susceptibility for non-Hispanic mothers who are either younger, have higher body mass index or lower educational attainment. Our case study is the first precision health study of critical windows.