How does someone gain a strong marketing management experience?

It is by way of experience, first you will star your career with executive level then manager then something different so by and by you will understand what is marketing and will also exploit the skill in that segment but i think all the things goes with your skill so if you have good skill then of course in short term of time, good experience can be attain.

Best way to learn is through low level exposure like work as sales executive and then  to maketing. Work for reputed company. Explore the core concepts of modern marketing management to develop your own effective customer-centric marketing strategy.