Even in the early days AI was heavily funded by the private sector. Symbolics machines were partly promoted as a way to do AI research, back in the logic era. And the AI winter was mostly a grant funding phenomenon. When it became unfashionable in universities the field rebranded as ML and became commercially driven by (mostly) different people. Companies like Google invested in advanced ML research from day one.

Nowadays it's been rebranded back to AI due to the switch to neural methods, but there's been funding for AI from the computer industry for as long as the field existed.

I'm pretty sure AI would exist as a field and be in a similar place to where it is now, even if governments had never funded it at all.