How many strong willed people have been 'broken' by their actions, finally admitting their way is not the best way? We have heard many instances of it as they turn to God or at least admit they are not as smart as they thought... Imagine if Trump came out and said 'that which is highly esteemed among men is abomination in the sight of God' and he has changed his stubborn ways while wearing a make the Kingdom great again hat. What a marvellous example that would be, but highly unlikely.
Do humans possess desires? Can a person who desires his own will instead of God's be changed by God? If he can't be changed why was he made that way? Do you pray for unbelievers?
Seeing as the will of man is depraved, bent and broken by sin, then leaving all things up to us would mean abandoning us to our own damnation. But God is unwilling that any should perish, but that we have everlasting life, and saves us. So, yes, God absolutely contravenes our will in order to save us, because He loves us.
If you see an infant starting to crawl out into traffic, you don't sit there and wait for the child to come to you, you run out into traffic and clutch that child into your arms to save and rescue it. The child might scream the whole way back, but so what? If you love that child you aren't going to let it just get run over.