How do I best position myself to get an NIH R01 grant?
For the NIH NIDCD (and likely other institutes, but I don't have the data), a great way to position yourself for an a new-investigator R01 is to first get an F32 post-doctoral fellowship since 70% of those with an F32 post-doctoral fellowship who applied for a subsequent RPG (predominately R01 and R03 awards) were successful. There might be better predictors, but 70% is pretty good when it comes to funding pay lines.

You should also be aware that the R01 club is not as closed as your question makes it sound. Historically, 25% of R01-equivalent awards are made to new investigators.