Due to the Army's downsizing, is it still possible to be "high-speed" and fast track through the enlisted NCO ranks?

Act like a rising star and you will eventually get rewarded for the exemplary behavior.

It absolutely is. Pay attention, do what's right, better yourself and contribute to the organization's overall end state. It will all pay off.

One thing about "who you know". Yes, who you know does play a part of career advancement, but it's more about the reputation you develop. If you are known as a hard worker and a competent Soldier, people will know. And at senior and nominative levels, believe me, people will ask their buddies about you before they take you on to their team.