1) Sponsorship/Mentorship. Will your current manager or another manager in the company champion your transition to a manager? Becoming a manager requires a lot of mentorship and coaching. Does HR at your company provide support? Is there a Senior Manager or Director that will mentor you?
2) Levelling. Does your company have a career ladder? Are there Staff Engineer levels? Have you reached this level as an IC? I personally would not sponsor an IC to become a manager if they haven't reached the Staff level. Staff Engineer is a sideways promotion to Manager. Senior Staff Engineer is sideways to Senior Manager.
3) Switching Companies. You should apply for a Staff Engineer position at a new company. During the interview process make it clear that you want to transition to a manager. During the negotiation phase, build a 6 month transition plan with the hiring manager.
4) Read. Read a lot. You should read all of the canonical management books.
https://www.amazon.com/High-Output-Management-Andrew-Grove-e... https://www.amazon.com/Managers-Path-Leaders-Navigating-Grow... https://www.amazon.com/Hard-Thing-About-Things-Building/dp/0... https://www.amazon.com/Making-Manager-What-Everyone-Looks/dp...
https://hbr.org/podcast/2019/08/the-challenges-and-triumphs-...
The Making of a Manager: What to Do When Everyone Looks to You
[1]: https://www.amazon.com/Making-Manager-What-Everyone-Looks/dp...
So a good answer depends a bit on what you're specifically interested in. But for a taste of things mostly at the tactical level, you might find value in something like:
https://www.amazon.com/First-Time-Manager-Jim-McCormick-eboo...
or
https://www.amazon.com/Making-Manager-What-Everyone-Looks/dp...