The prediction of the martensite start temperature ($M_s$) for all steel alloy types based solely on their chemical compositions is a complex problem. Previous works applied thermodynamic and machine learning models successfully within limitations, such as focus on certain steel types or by executing additional feature engineering. This encouraged us to overcome existing limitations and improve the $M_s$ prediction accuracy for all steel alloy types in a single model. Two publicy available datasets were merged and cleaned, retrieving a total of 1800 entries with up to 15 chemical elements including all types of steel alloys ($M_s$ ranging from 150~K to 790~K). The training-validation dataset was formed of 1500 randomly selected entries. The remaining 300 entries form the large, final test dataset. Extensive hyperparameter tuning was performed to find the best artificial neural network (ANN) for this dataset. Each model was evaluated using a 5-fold cross validation approach. As a reference the predictions of 37 thermodynamic models against all entries were calculated. The best model achieved a mean average error (MAE) of 26~K with a standard deviation (SD) of 45~K. The best ANN, consisting of two hidden layers with a total of 5000 trainable params, finally achieves a MAE of 17~K with a SD of 20~K on the test dataset, an improvement by 9~K (+35%) and 25~K (+56%) respectively. This work presents i) a simple machine learning approach without feature engineering, which ii) achieves higher overall accuracy than existing thermodynamic models to predict the $M_s$ while iii) at the same time not being restricted to certain steel types, removing the need to know which model predicts best for a certain steel alloy. Additionally, the explainable AI method SHAP is used to estimate feature importance for the developed model. Lastly it provides a new publicy available dataset, which will be, together with the code and model, available at: \url{https://github.com/EAH-Materials}.