Atmospheric blocking events drive persistent weather extremes in midlatitudes, but isolating the influence of sea surface temperature (SST) from chaotic internal atmospheric variability on these events remains a challenge. We address this challenge using century-long (1900-2010), large-ensemble simulations with two computationally efficient deep-learning general circulation models. We find these models skillfully reproduce the observed blocking climatology, matching or exceeding the performance of a traditional high-resolution model and representative CMIP6 models. Averaging the large ensembles filters internal atmospheric noise to isolate the SST-forced component of blocking variability, yielding substantially higher correlations with reanalysis than for individual ensemble members. We identify robust teleconnections linking Greenland blocking frequency to North Atlantic SST and El Niño-like patterns. Furthermore, SST-forced trends in blocking frequency show a consistent decline in winter over Greenland, and an increase over Europe. These results demonstrate that SST variability exerts a significant and physically interpretable influence on blocking frequency and establishes large ensembles from deep learning models as a powerful tool for separating forced SST signals from internal noise.