I'm not the person you responded to, but I did also recently make a transition from an individual contributor role into a management role and can share some experiences.

In addition to taking on more leadership roles in engineering projects, I began finding and taking on opportunities on the side that have a managerial element to them, for instance recruiting (sourcing, behavioral interviews, selling candidates, redesigning our interviewing processes), mentoring/coaching people, driving our company's internship program, etc. I found that I enjoyed that sort of nontechnical work. In particular, I liked thinking about how to grow other people and help them be effective.

I vaguely started thinking that I wanted to just switch into management, and I advertised that fact (mostly to managers). I wasn't too urgent about it, and an opportunity showed up [after a few months] and the management team thought of me first as someone who could be a good fit. Part of what made it a good fit was that the team was not 'on fire' or anything, so if I were to do a bad job or realize I didn't like management and thus needed to switch back, the company wouldn't be in a particularly bad situation.

Sadly, I have not bridged that gap (YET!). In the past I've made lateral transitions into product management and project management, but these roles, like "engineer" are individual contributor roles and have similar career limitations.