Catchment transit times are often inferred by assuming a transit time distribution (TTD) or a SAS function and calibrating their parameters against measured tracer data. In the presence of high-resolution tracer data, machine learning tools may offer a promising avenue for advancing TTD estimation by leveraging data-driven approaches, integrating diverse data sources, and improving accuracy, scalability, and adaptability. Here, we lump together ideas coming from Large Languages Models, survival analysis and sum of squares techniques to introduce a novel data-driven model for estimating TTDs. Our model is influenced by SAS-based approaches; however, unlike previous studies, we avoid imposing strong parametric assumptions on the SAS function. We showcase the performance of our model against a benchmark of eight virtual datasets that differ in precipitation amounts, seasonality and runoff flashiness. We find that machine learning methods may effectively predict solute concentration in streamflow yet struggle to accurately estimate the true TTDs. However, when the appropriate inductive bias is incorporated, numerous key aspects of TTDs, such as the young water fraction and the average TTDs, can be estimated robustly. We also identify settings where the estimation task is more challenging for our model. This analysis, based on reproducible virtual benchmarks, provides a first overview of machine learning capabilities in estimating TTDs and inspires future TTD model inter-comparisons.