How to get my next position of managing 50+ people?
To go from managing a team of 4 to "50+" is quite a large step and it may not be reasonable to think of it as "your next position" since often times a "team" has a "lead", several teams have a "manager" (you are now at 15-25 people) and then several managers have "directors" (the 50+ mark). The titles might be different, but the structure similar.
You mention your technical skills in your question, but do not offer any managerial skills besides to frame your experience as "managed no more than four people." Non-technical people need to see people skills and managerial focus, since dealing with people problems as a manager is not at all like dealing with technical problems. You cannot "debug" an employee that is chronically late to work in the morning, or "write a script" to do a presentation to investors.
Typically technical career advancement follows two disparate tracks - "manager" and "architect" where a manager focuses on developing people management skills while an architect focuses on solving ever increasing system design complexity.
You seem like you are trying to justify an advancement down the "manager" track by developing and promoting your technical skills. This will not work since more advanced techno-speak does not help a CEO, VP, Director, customer, lender or other non-technical colleague work better with you managing teams, communicating needs, handling management problems, etc. with large groups.
What steps can I take?
It might help to highlight your soft skills/people skills in your question so that you can get more specific advice. Also, understanding and being able to communicate strengths and weaknesses in your soft skills is also important, since anyone non-technical that is interested in hiring you will be very familiar with that kind of evaluation.
For example, when you were selected as CTO for a start-up, if your resume only focuses on technical challenges then you miss out on an opportunity to showcase your communication and managerial challenges. For example, as CTO you may have had competing technical viewpoints that must be managed both internally (developing a system for keeping the direction and goals of the company in focus while hiring new talent) and externally (communicating technical progress and goals to other managers, investors, important customers, potential partners, etc.).
A resume that has "CTO" as a title but then a job description of "built a system to..." or "created a prototype..." is certainly expected for a start-up, but if it lacks key points like "helped develop and maintain technical budget" or "provided technical support and requirements gathering during customer visits" or "gave progress updates to current and potential investors" then the soft-skill component of the job was neglected, and I would be concerned that such a CTO did not develop "management skills" during the time at the start-up. Budgeting, communication and presentation skills are required to break from a develop/team lead to a manager/executive.
The value of experience in these soft skill areas increases exponentially as the number of people you manage grows. As your management responsibilities grow there is then the challenge of maintaining respect with your technical subordinates and keeping skills current when the majority of your time is spent communicating and managing. Highlighting how you handle those problems is one strong indicator of a skilled technical person that is developing managerial skills as opposed to architectural skills.
Hope that helps.