>>NATO was created before the Cold War
The North Atlantic Treaty was signed in 1949. George Kennan's 'long telegram' was 1946 - so I'd guess this comes down to when exactly you consider the cold war to have started. IMO, there was already a conflict during German partition.
That said, the point of NATO was to keep the US involved in Europe. We'd turned away after Versailles - and that didn't exactly turn out well.
I've had some conversations about this with a friend who's a history professor (emeritus) who'd specialized in the Cold War. He was of the opinion that it started as the US broke some promises around control of the partitions. At the time, I was mostly interested in classical history (had been working my way forward from Herodotus), but I got sucked into this period because it's so interesting.
Oh, and Iceland was all about SOSUS. I worked with one of the guys who wrote analysis code to turn that into positional info.
As far as NATO trying to antagonize Russia, I see it as more like the way the Roman Empire grew. Many nations wanted to join - for protection from their enemies (part of the deal was that Rome would consider your enemies theirs - held whether joining was voluntary or not). There's clearly an enemy the new states are looking for protection from. I'd agree that they are antagonizing Russia - this is more about intentionality.