He had to know we’d annihilate him if the US, Canada, UK and Australia and whomever else decides to get more personally involved say after he targets western cities.
It's doubtful that Putin's regime would actually bomb Western cities anyways. As it stands, they have no allies. China's economy is heavily reliant on trade with not only North America, but Japan and Europe. India is mostly self-sufficient and has been abstaining from involving itself in Russia's war. Belarus is basically Russia's only true ally atm.
If Russia decides to bomb Western cities, genuinely, it would mean the end of Russia as a state; the oligarchs and wealthy politicians who actually have the power will actually negotiate with the West to keep *their* portion of Russia. Essentially, Russia going to war with NATO will mean the stratification and dissolution of the Russian Federation in favor of separated states run by a new wave of despots and monarchs. Frankly, that's far more manageable too.