Cloud formations often obscure optical satellite-based monitoring of the Earth's surface, thus limiting Earth observation (EO) activities such as land cover mapping, ocean color analysis, and cropland monitoring. The integration of machine learning (ML) methods within the remote sensing domain has significantly improved performance on a wide range of EO tasks, including cloud detection and filtering, but there is still much room for improvement. A key bottleneck is that ML methods typically depend on large amounts of annotated data for training, which is often difficult to come by in EO contexts. This is especially true when it comes to cloud optical thickness (COT) estimation. A reliable estimation of COT enables more fine-grained and application-dependent control compared to using pre-specified cloud categories, as is commonly done in practice. To alleviate the COT data scarcity problem, in this work we propose a novel synthetic dataset for COT estimation, that we subsequently leverage for obtaining reliable and versatile cloud masks on real data. In our dataset, top-of-atmosphere radiances have been simulated for 12 of the spectral bands of the Multispectral Imagery (MSI) sensor onboard Sentinel-2 platforms. These data points have been simulated under consideration of different cloud types, COTs, and ground surface and atmospheric profiles. Extensive experimentation of training several ML models to predict COT from the measured reflectivity of the spectral bands demonstrates the usefulness of our proposed dataset. In particular, by thresholding COT estimates from our ML models, we show on two satellite image datasets (one that is publicly available, and one which we have collected and annotated) that reliable cloud masks can be obtained. The synthetic data, the collected real dataset, code and models have been made publicly available at https://github.com/aleksispi/ml-cloud-opt-thick.