I am pessimistic about such ideas.
First of all, the course of action would not, in any way, shape or form, "preserve the territorial integrity of Ukraine", and I have grave difficulties to believe that you actually mean this. Isn't it glaringly obvious that the Russians will not retreat entirely? Is it not totally obvious that this would encourage Putin to stay indefinitely? As things stand now, perhaps Putin's goal is a) regime change, b) territorial gains in and between Donbas and Crimea c) then retreat and enjoy a weak Ukraine. If NATO moves into Western Ukraine, Russia will definitely stay in all of the East, at least up to the Dnjepr.
I said "
help preserve the territorial integrity of Ukraine".
I mean, if NATO protects the Western part of Ukraine, after an invitation by the legitimate authorities of this country, one may reasonably hope that Putin would no longer try to conquer the whole of Ukraine, with devastating consequences, in terms of destructions, millions of refugees and so on.
The great military power of the United States would then have a useful purpose, without firing a single shot or endangering a soldier, since there are no Russian troops where NATO would go.
This would of course have nothing to do with Putin's brutal conquest, war of agression, shelling of civilians and civilian infrastructure and so on, the Russian-speaking minority there (see
https://en.wikipedia.org/wiki/Russian_language_in_Ukraine#Current_usage_statistics) would have their rights maintained, they wouldn't be subject to persecution.
Without directly joining NATO (which, I think, would be too provocative with respect to the Russian president), Ukraine could sign a treaty of friendship and mutual assistance with NATO, which would imply a rapid deployment of NATO troops upon request by the Ukrainian government (in areas which are not occupied by the invader).
In the mean time, NATO could perhaps provide Ukraine with the requested warplanes (
https://www.tbsnews.net/world/zelensky-tells-nato-send-us-planes-379504).