A complete understanding of the sources of predictability for atmospheric behavior at the subseasonal-to-seasonal (S2S) lead times is crucial for improving current prediction systems; this knowledge would allow future theoretical, modeling, and observation efforts to focus accurately on representing specific Earth system processes that are relevant for tackling this problem. In recent years, machine learning methods, and specifically, convolutional neural networks (CNNs), have shown potential not only for forecasting atmospheric processes at the S2S time scale with reasonable skill but also for extracting knowledge from the data that is complementary to the scientific state-of-the-art of atmospheric predictability. In this study, we utilize this potential by building a set of CNNs that predict the probability of different Weather Regimes (WRs) occurring over North America for lead times from weeks 2 through 8. The WRs are defined using k-means clustering of geopotential height fields at 500hPa, and the CNNs are trained separately with fields of variables corresponding to different Earth system components (atmosphere, ocean, and land) as inputs. Despite the prescribed limitation of each model using only one variable as input, their skill is still competent compared to the benchmarks of persistence and CESMv2 forecasts. Based on performance analysis and after a thorough hyperparameter optimization, we assess the relative importance of each input variable for this specific prediction problem and its variability across different dimensions. Given the significant relative relevance changes identified within the results, this study highlights the importance of considering S2S predictability contributions from different Earth system components depending on the lead time of interest, season, and initial WR when predicting large-scale atmospheric behavior at the S2S time scale.