Marin will officially become PM in a few days when the parliament elects her for the office; the coalition parties have already agreed. At 34, she will become the youngest female Prime Minister in the world, certainly at the moment (she's younger than Jacinda Ardern), maybe ever?
Depends on if you count Captains Regent of San Marino (there have been one 26-year old, two 27-year old and one 28-year old women to serve as that). If not, then Marin is the world record-holder.
Let’s only count real countries ...
Once Kurz gets sworn in again, he will be the youngest worldwide again (currently it’s the Ukrainian PM).