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Machine learning (ML) and in particular deep learning (DL) methods push state-of-the-art solutions for many hard problems, for example, image classification, speech recognition, or time series forecasting. In the domain of climate science, ML and DL are known to be effective for identifying causally linked modes of climate variability as key to understand the climate system and to improve the predictive skills of forecast systems. To attribute climate events in a data-driven way, we need sufficient training data, which is often limited for real-world measurements. The data science community provides standard data sets for many applications. As a new data set, we introduce a consistent and comprehensive collection of climate indices typically used to describe Earth System dynamics. Therefore, we use 1000-year control simulations from Earth System Models. The data set is provided as an open-source framework that can be extended and customized to individual needs. It allows users to develop new ML methodologies and to compare results to existing methods and models as benchmark. For example, we use the data set to predict rainfall in the African Sahel region and El Niño Southern Oscillation with various ML models. Our aim is to build a bridge between the data science community and researchers and practitioners from the domain of climate science to jointly improve our understanding of the climate system.