It’s actually very simple to prove that everyone will eventually repent and believe the Gospel. You see, the word “repent” simply means “to change one’s mind.” And so, even if someone doesn’t change their mind about how one is saved and come to believe the Gospel (which is the good news that Christ died for our sins, that He was entombed, and that He was roused the third day) before they die, after they’re resurrected from among the dead at the Great White Throne, they’ll certainly change their mind about salvation at that point (meaning they’ll have “repented”), and will also pretty much certainly finally believe that Christ did indeed die for their sins, and that He was entombed and was roused the third day, at that point (it would be hard to deny when Christ is standing in front of them).
So even if someone thinks that people definitely have to “repent and believe the Gospel” in order to experience salvation (because they don’t understand the difference between salvation from an absolute perspective, salvation from a relative perspective, and salvation from a physical perspective), it seems like a pretty sure thing that everyone will have repented (changed their mind about salvation) and believed the Gospel at that point, which means everyone would eventually get to go live on the New Earth at some point, if that’s how one actually gained the salvation Paul primarily taught about (which it isn’t, as explained in my free eBook, but that’s a whole other discussion).