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Plan to make a transitional stop as a team lead. It's a position that lets you develop "leadership" skills and practice interfacing with managers and other departments on behalf of a team. But it's still an engineering position and doesn't require previous management experience.

At a smaller company (most early stage startups) with a team of 10-20 engineers is where you're most likely to get the most management exposure as a team lead. Because the engineering team is big enough to need a leadership and planning layer below the CTO but too small to have developed a true management army yet.

In a small company (run well), you'll also have more exposure to how your decisions impact the business and what business information you need to make those decisions - crucial aspects of being a good manager.

However, a larger company is more likely to have good mentors for you to learn from. Like everything else, it's a trade off and a balancing act. You may want to try both routes.

If you find you like it and you're pretty good at it, it should be much easier to get hired into a management position from a team lead position than from a plain engineering position because you've positioned yourself as a leader of people and have some practice doing it.

Then you just need to be confident that you'll be content spending 95% of your time talking and planning and 5% or less working directly with the tech.