This could be applied to the current situation as well in a way.

If Russia wanted to invade Poland and Romania to plug the gaps this would be the perfect way to do it. Right now they have their peace time force wearing down the Ukrainian army and pulling in western equipment which as time goes on is weakening the west but also this galvanises Russia herself, Russia would not have been able to start a full-scale war against NATO a year ago or maybe even now, the popular support would not be there. But as the war goes on Russian society starts adapting to the new norm, in addition to that they are seeing NATO assistance in Ukraine and are seeing how NATO essentially is already in conflict with them, many might feel like NATO is the aggressor and NATO wants to destroy them and the Russia media would have an easy time of spinning that tale with some of the rhetoric that has been said by Biden and others so far. Russia could keep this going for a few months, drawing in more western equipment, causing relations to get even more heated between NATO and the west and getting the population even more relied up. Then they could mobilise the entire Russian army under some pretext about protecting the newly incorporated Donbass regions of Russia, saying they are going to defeat Ukraine and that the only way this can end is if Ukraine is conquered entirely. Only once they reach Lviv, they just keep going.

And of course the longer this war goes on the more of a chance there is that NATO might send troops or do something else that might escalate it to a war, there is that too. And then you could say the US expected all this and actually wants it to happen.