If faith is "God-supplied" then the crucial issue is who God chooses to supply this faith to and how He decides to do so.
If there are any criteria at all then it is by those criteria that our salvation is decided. And it is, again, the case that some people will narrowly miss meeting those criteria while others will scrape through.
If there are no criteria at all then you have salvation by lottery, but even then you do not escape the problem. Suppose God decided to save one more person. There must be some person who would be saved - and thus they have narrowly missed salvation because God decided to save 1 fewer person - or is it impossible for God to save any more ? Equally there must be some method of generating the identities of who the lucky people are to be - by that token everybody who is saved only narrowly scrapes through and many more people narrowly miss.
Finally if salvation has nothing to do with human belief or human actions what is the point of Christian preaching or attemtps to convert ? Why did Christianity have to start with a few preachers in Judaea and spread through the world by human means ? If people who have heard the preaching are not at an advantage in reaching salvation then what good is it ?