How is a mere six months going to do that?
Cesare's position after Alexander's death suggests less "brink of success" and more "only by the favor of his father".
I'm open to someone who knows better than me proving me wrong - I'm no expert.
But it strikes me as "Yeah, another six months of the most hated pope of his century."
Yes, absolutely, Cesare depended on the favor of his Father to to get on the road to power. At the time of Alexander's death, Cesare's star was still rising.
I stated 6 months as a bare minimum, as many of his conquests in central Italy were quite fresh and absorbing Tuscany (if he could) would need time, as well. It's a stab at guessing a bare minimum, but it would be natural to conclude that the longer a friendly pope is on the throne, the farther Cesare gets and the more his power grows.
It's a further 6 months of consolidation and opportunity that doesn't exist when (and of course, if, allowing for butterflies) della Rovere (who was the nemisis of the Borgia) gets the keys to St. Peters. Cesare seemed to be on verge of great things concerning developing a self-sufficient power. What seemed to be critical to his success was there not being a hostile Pope on the throne that his enemies could rally around as much as working under a pope who sustained Cesare's privileges . OTL, Alexander's immediate successor, Pius III, during his short reign, maintained Cesare's rank and standing. This was Cesare's worst luck -- the fact that Pius didn't last longer than he did.
Ultimately, as in my prior post, I posit Cesare's long term prospects as a possibility. Not a sure thing, to be sure.