Mentoring students - Computer Science I am interested in mentoring students (undergrad / MSc) in areas of Artificial Intelligence and Software Engineering. 

Unfortunately, the university I graduated from/ currently work at do not offer such mentoring programs; however, this is a valuable experience that I wish to gain.

I appreciate any suggestions.
To answer with something fully external to your university:

Google Summer of Code

Google Summer of Code is a program that is about getting university students (undergrad or postgrad) contributing to open source.

Some open source project can be very technical/scientific.
I've mentored this year and last for JuliaLang/NumFocus.
Since Julia is a language primarily aimed at researchers, many of our projects are very technical.
The project I co-mentored last year was literally to implement and improve an algorithm from a paper.*

JuliaLang runs a bunch of AI projects each year.
I am sure the R and Python communities do too.

*Lagaris, Isaac E., Aristidis Likas, and Dimitrios I. Fotiadis. "Artificial neural networks for solving ordinary and partial differential equations." IEEE Transactions on Neural Networks 9, no. 5 (1998): 987-1000.