Nato expansion was done long before Putin stated this war. All the Eastern European nations bordering or near-bordering Russia were Nato almost 20 years ago.
Your analysis is incoherent.
The Biden administration, moreover, was bending backwards to accommodate Russian interests, and those of its Euro allies, the German “deep state”. The approval of Nordstream 2 was a critical move.
Rather, it seems that the Russians took the opportunity to attempt their coup de main precisely because the US administration exuded weakness.
The US administration was doing nothing wrt Ukraine that wasn’t already going on under Trump. US policy in 2021-22, other than the weakness above, was entirely status quo. The “gamble” was entirely Russian.
When you live in an world where you only have a conversation amongst your NATO peers and Western friends, are only concerned about your Western economic and political interests, (((and you entirely exclude and discount someone else’s concerns))), you end up with a war.
There was no Russian threat until we initiated by doing what we said we would not do (NATO East expansion into former Soviet border states) and where they stated for a long time that this is a no-go for them: NATO expansion into Ukraine.
Biden offers NATO to Ukraine in October 2021: https://www.reuters.com/world/europe/ukrainian-president-zelenskiy-holding-talks-with-biden-adviser-says-2021-12-09/
By November 2021 Russia is building up forces along the Ukrainian border, 92,000 additional men and holding large scale maneuvers and live fire exercises: https://foreignpolicy.com/2021/11/01/us-russia-military-movement-ukraine/
I am not sure how more “cause and effect” it can be?
We didn’t bend any direction for them. We just entirely ignored them and did whatever we wanted.