When you bring up the fact that Scripture teaches the eventual salvation of all humanity, many Christians will attempt to object by saying that it can’t be true because it would violate our so-called “free will.”
The thing is, whether or not “free will” exists, it just doesn’t matter when it comes to salvation, because the choice isn’t about getting saved vs not getting saved in the first place. The actual choice (at least as far as Paul’s Gospel goes) is about experiencing salvation early vs experiencing salvation at the end of the ages.
The confusion arises because most Christians assume that people have to decide between “accepting Jesus as their personal saviour” or being damned for eternity, when the choice is actually between A) believing that God will save everyone through what Christ accomplished, and getting to enjoy that salvation early if you believe this Good News, or B) not believing this Good News and having to wait until the end of the ages to experience salvation.
The thing is, the Good News which Paul taught isn’t that you can escape never-ending punishment if you believe the Gospel now, as most Christians have mistakenly assumed it to be. The Good News (well, the end result of the Good News) is that you will experience salvation because of Christ’s death for our sins, and His subsequent burial and resurrection. And if God happens to gift you with the faith to believe what this Good News means now, you’ll get the special salvation Paul wrote about in 1 Timothy 4:10, which is an early experience of that salvation (which is ultimately about immortality and sinlessness, not about escaping a torture chamber called hell).
To put it another way, the Good News isn’t that you can escape never-ending punishment if you happen to choose to believe the Good News that you can escape never-ending punishment. (Think about it, that’s what the traditional Christian message actually is: believe the Good News and you’ll be saved from “hell,” with the Good News you need to believe being that you can be saved from “hell” if you believe the Good News that you can be saved from “hell” — it’s an entirely circular doctrine if you really break it down, although almost no Christian ever does.) In actuality, the Good News is simply that you will be made immortal and sinless because Christ died for our sins, and because He was buried and resurrected; and if you happen to believe this Good News, you’ll even get to experience said immortality and sinlessness earlier than everyone else will (but you will still experience it eventually regardless).
This means, I should add, that very few Christians have been saved yet (at least from a relative perspective; everyone can be said to be saved from an absolute perspective because of what the Gospel means). Because you can’t believe something without understanding what it means, and because very few Christians have actually understood what the Gospel really means, we have to conclude that most Christians haven’t actually believed the Gospel at all, which means they haven’t been saved yet (although they will be saved eventually, of course, because of what the Gospel means).
Oh, and before someone brings it up, yes, there are passages which teach us that not everyone will be saved, and they’re equally true to what I wrote above. The reason for that, however, is that they’re talking about an entirely different sort of salvation from the one Paul wrote about, as I explained here.
As for those who are reading this and aren’t familiar with the fact that the end result of Paul’s Gospel means that everyone will eventually be saved, I’ve written about this in various places on this website, but I’d suggest beginning with the following three articles to get started on your understanding of the true meaning of his Gospel: