Checking if ML model is possible
When in doubt simply build a model and test how good it is (accuracy, MSE, whatever).

If those KPIs are not up to par, think about improving the parameters, feature engineering, etc.

I find this approach to be more valuable than to spend a lot of time analyzing correlations and other classical statistical analysis.

If simple models (Regression, GLM, RandomForest, XGB) do not produce results with any sensible accuracy and you see no path to successful feature engineering then you have your answer as well.

The only downside to this approach might be a perfectly good model on the first try ;)