It depends what you mean by “non-Christian”.
When Adam and Eve disobeyed God, sin entered the world, and the gates of Heaven were closed to us. They had everything we complain about not having spiritually- frequent, obvious contact with God, one-on-one attention, clear cut divine directives. And they STILL chose to place their desires over God’s. Because of that, because they told God through their actions, “Never mind you, WE’RE the real gods”, humanity lost Heaven. Nothing we could ever ever do would make up for that original sin against God. A huge, uncrossable gulf was created between us and God.
That’s why Jesus had to come. When God entered the world, becoming one of us, submitting Himself entirely to Divine Will, and willingly taking our death, our punishment upon His perfect shoulders, He became that bridge we needed to cross the distance between us and God.
So while there are things Jesus clearly commanded us to do in terms of our salvation, none of it is possible without Him as the bridge. Without Jesus’ sacrifice, there is not a single person ever born who was “good enough” to bridge that gap between us and God.
Now, the Church doesn’t teach what happens at the point of death. We do know that we are all God’s creations, and that we’re invited to be the adopted children of God through Jesus. Is it possible that at the moment of death, every soul is given the ultimate chance to know and embrace Christ? That the “non-Christian” has a chance to become Christian? Well, nothing is impossible through God.
But if a soul IS given that chance, and still denies the necessity and effect of Christ’s sacrifice, it’s like a person seeing a bridge crossing a bottomless pit, refusing to use the bridge, preferring to jump instead, and wondering why they don’t make it to the other side.
I hope this makes some sense.