GS13-15 can also be achieved for sustained technical excellence and innovation. (My own career path was unusual, in that I took on technical and management challenges at different times).
As I mentioned, a lot depends on OP's knowledge domain, the agency or department OP plans to join, and the current climate at said agency. Presumably, OP has already factored in his/her best guess about all those things.
I guess what I am saying: promotion to GS13-15 is NOT automatic. GS11 to GS12 can be achieved on technical skills alone..or "what" you know.
Promotion to GS-13-15 are management positions so office politics is partially a factor and it really depends more on "Who" you know. Normally there is a promotion board of managers who interview the GS12 candidates for the vacant GS13-15 position to give every GS12 candidate an opportunity.
When I went to Afghanistan as a Civilian, promotions were relatively easy simply because it was a combat zone so it was difficult to get Civilians to volunteer to go to Afghanistan and therefore less competition. However, back in the states, he may have a dozen GS-12 candidates applying for a single GS-13 vacant position. Unless OP is REALLY good he has to convince the board members that he is the most qualified candidate.
In your case, you were savvy enough to get the GS13-15 position. However, OP may have not the skills that you have. On the other hand, if OP is very knowledgeable and competitive, then that is his determination.
Remember that he want to reach that level in less than 12 years so he must be management material to begin with. This means public speaking skills, ability to talk intelligently to upper management, ability to supervise lower GS personnel, making things happen quickly, meeting schedule deadlines, looking good during a management meeting and looking good during a public meeting with the news media attending that public meeting.