Abstract The Madden–Julian Oscillation (MJO) and stratospheric polar vortex (SPV) are prominent sources of subseasonal predictability in the extratropics. It has been shown that the joint interaction of the MJO and the SPV can modulate the preferred phase of the North Atlantic Oscillation (NAO) and the occurrence of weather regimes. However, improving numerical weather prediction (NWP) at 3‐week lead times remain underexplored. This study investigates how MJO and SPV phases affect Greenland Blocking (GL) activity and integrates atmospheric state information into a neural network to enhance week 3 weather regime activity forecasts. We define a weather regime activity metric using European Centre for Medium‐Range Weather Forecasts (ECMWF) reanalysis and reforecasts. In reanalyses we find increased GL activity following MJO phases 7, 8, and 1, as well as weak SPV phases, indicating climatological windows of opportunity in line with previous studies. However, ECMWF forecast skill improves only in MJO phases 8 and 1 and weak SPV phases, identifying somewhat different model windows of opportunity. Next, we explore using these findings in postprocessing tools. Climatological forecasts based on MJO/SPV–NAO relationships provide a purely statistical approach to subseasonal GL activity forecasting, independent of NWP models. Notably, MJO‐conditioned climatological forecasts show clear signals when evaluated against observed GL activity. Statistical–dynamical models, using neural networks that combine historical atmospheric state data with NWP‐derived weather regime metrics, improve weather regime activity forecasts across all regimes considered, achieving an absolute accuracy increase of 5.8 percentage points in forecasting the dominant weather regime compared with ECMWF. This is particularly beneficial to blocking in the European domain, where NWP models often underperform. Atmospheric conditioned and neural network forecasts serve as valuable decision‐support tools alongside NWP models, enhancing the reliability of subseasonal predictions.