if there are zero automated tests, things probably weren't written with (automated) testing in mind, so there may be a lot of coupling... starting off with integration tests just to validate existing behavior is a good start. hopefully the existing applications aren't also inextricably bound to environments that are run on pet servers and managed by other teams...
I got this a few years ago. When I solved most of the questions, it asked for my contact info and Google reached out for an interview... which involved someone watching you code in a google doc, which distracted me so much I bombed