DSGE models aim to be explanatory models of an economy. They are not the best at predicting (bayesian VARs do better forecasting, there is a tutorial on it in my quant econ link) but they turn out to do forecasting decently well, too.

The reason that is is that purely statistical/predictive models of macro are subject to the Lucas Critique [1]. It says roughly, if you observe an economic relationship is happening, but you don't have an explanatory reason why it is, it's a bad idea to use it for policy prescription.

The NY fed model has a whitepaper here [2], which should be accessible to the technical data scientist (technical, but not prohibitively so).

Their readme points to a few posts on using it, I think the open source code comes with a csv for example input data. There should be publicly accessible macroeconomic data in a few places for you to play with it, say at FRED or the World Bank. I think Julia has a Stata-style api package for FRED data, making the data processing easier.

Have fun!

[1]https://en.m.wikipedia.org/wiki/Lucas_critique

[2] https://www.google.ca/url?sa=t&source=web&rct=j&url=https://...