Capitalizing on the recent availability of ERA5 monthly averaged long-term data records of mean atmospheric and climate fields based on high-resolution reanalysis, deep-learning architectures offer an alternative to physics-based daily numerical weather predictions for subseasonal to seasonal (S2S) and annual means. A novel Deep UNet++-based Ensemble (DUNE) neural architecture is introduced, employing multi-encoder-decoder structures with residual blocks. When initialized from a prior month or year, this architecture produced the first AI-based global monthly, seasonal, or annual mean forecast of 2-meter temperatures (T2m) and sea surface temperatures (SST). ERA5 monthly mean data is used as input for T2m over land, SST over oceans, and solar radiation at the top of the atmosphere for each month of 40 years to train the model. Validation forecasts are performed for an additional two years, followed by five years of forecast evaluations to account for natural annual variability. AI-trained inference forecast weights generate forecasts in seconds, enabling ensemble seasonal forecasts. Root Mean Squared Error (RMSE), Anomaly Correlation Coefficient (ACC), and Heidke Skill Score (HSS) statistics are presented globally and over specific regions. These forecasts outperform persistence, climatology, and multiple linear regression for all domains. DUNE forecasts demonstrate comparable statistical accuracy to NOAA's operational monthly and seasonal probabilistic outlook forecasts over the US but at significantly higher resolutions. RMSE and ACC error statistics for other recent AI-based daily forecasts also show superior performance for DUNE-based forecasts. The DUNE model's application to an ensemble data assimilation cycle shows comparable forecast accuracy with a single high-resolution model, potentially eliminating the need for retraining on extrapolated datasets.