Nuclear is sustainable though, we can sustain it for the forseeable future - many generations. Fossil fuels are not sustainable, their supply is more limited and the consequences of pollution too severe.
Nuclear is not renewable, but it is sustainable and not polluting so it fits into the category of "green".
However, nuclear is not quick. Like you say, we're already late to the party when it comes to fixing things. Using money and resources for nuclear over renewables may end up taking longer to get to net zero than just going hard on renewables and transmission first (although the specific circumstances do vary widely by region/nation).