Carlsen can't beat AlphaZero in an actual game
Statistically seen for the limes of many games, that's surely true. But it's not true to say a priori, Carlsen had a theoretical 0% chance for a win. To see that, one for instance can refer to several anti-computer approaches (Nakamura is an expert here :) ) that were successful even for quite modern Stockfish-versions at least, often exposing implementation bugs but sometimes really showing the limits of deep-search algorithms (calculation horizon). Alpha-Zero might be something special here (depending on its operation-mode) since it's able to learn from previous mistakes in general. So while (some) successful chess engines from decades ago would have done the same mistake again and again, allowing even a tournament win for a human grandmaster, I doubt that this would be possible for a live adaptive version of Alpha-Zero anymore.
but what if we gave him the ability to takeback any blunder or
sub-optimal move he makes and try again?
That won't be enough for the most cases, maybe it would highly increase the draw-rate only. Carlsen would not just have to look for obvious blunders, but for very subtile unprecise decisions too, where the consequences can often arise late in the game. At the level of Alpha-Zero, that might often require a computer-based post-mortem analysis at least.