The logical end of Calvinism... "No, I'd say God doesn't wish for everyone to be saved."
Again a verse cherry picked from its surrounding text, Paul is not teaching the natural man cannot understand spiritual things, what he is saying in context is that spiritual things cannot be understood through human wisdom and philosophies.
He speaking to people of the Greek culture who held human philosophy in high regard.
Paul makes it clear here that the sacred writings can give the wisdom that is needed....
“…from childhood you have known the sacred writings which are able to give you the wisdom that leads to salvation through faith which is in Christ Jesus. All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness…” (2 Tim. 3:15-16)
And yes people do and are able to seek after truth of their own volition and agency, the problem is human philosophies get in the way not because a person has no ability to understand.