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I made a move like this in the past through a recruiting agency. I was very specific about what I was looking for, and about 4 months later they sent me an oppertunity that looked like a fit, I interviewed then took the job.

Doesn’t hurt to be friendly with a few recruiters

You get into a para-managerial role in tech first, then leverage the new job title to get a more purely-managerial role elsewhere, emphasizing the organizational elements of your experience.

I recently switched from tech to education by emphasizing the educational parts of my previous jobs, which were otherwise very technical.

It was surprisingly simple, even though they were non tech (utility company) they still needed data processing, scripting, and some basic ML work, especially in their marketing team. Same kind of work, however to a more credulous senior management team. Their main problem was they didn't know what could be done, let alone how to do it.