Triggering what? It's not like the UK has the capability - every "strategic defence review" is just cut, cut, cut. Challenger2, AS90, cut to the bone. Typhoon is barely capable of air-to-ground and the Tornado fleet is rapidly approaching end of life. The Type 45s fitted "for but not with" their major weapons. Carriers without anything to carry.
NATO cannot defend the Baltic States, and if push comes to shove, it won't even try.
As far as I know the plan against a Russian tank rush now is the same as it was when it was the Fulda Gap[1] they were protecting: tactical nukes.
And I think you underestimate NATO power and overestimate Russian. Russia does have a lot of tanks, but the vast majority of them are T-72s and older[2], which are sitting ducks for modern shoulder-launched anti-tank missiles.
Despite that, they do have a lot of T-90s, which are a good tank. But the disparity isn't as high as a first glance makes it appear, and NATO does have better air forces (the F-16 isn't as obsolete as you seem to think).
NATO cannot defend the Baltic States, and if push comes to shove, it won't even try.