Starting from being a newly minted private pilot, what are the steps I would have to accomplish in order to eventually qualify for and compete in the Red Bull Air Race? Assuming I put most of my time into the endeavour and progressed at a reasonably fast pace, how long would it take me?
According to their about page
New pilots who wish to participate in the World Championship must first fulfil the minimum criteria set by the Red Bull Air Race Committee, which include top achievements in international flying competitions organised by the FAI. They must also be active aerobatic air display pilots. Eligible pilots that prove their skills at the Red Bull Air Race Qualification Camp can achieve the Red Bull Air Race Restricted Superlicence. Once they have the Restricted Superlicence, they then qualify to take part in the Red Bull Air Race World Championship in the Challenger Cup.
So I would suggest if this is something that interests you, you begin with some instruction in aerobatic flying - a discipline which in itself is quite tough. To find the next qualification camp, I would suggest contacting red bull air race directly. It seems they run annual qualifications, most recently held in Texas, USA.
The amount of time it would take is impossible to measure, or even speculate.