I doubt that there is such a final proof. The weight of scripture seems to me at least to support UR but obviously not sufficiently to convince the majority - of evangelicals, say. One reason may be that the average Christian may not read and study the subject for themselves, preferring to rely on pastors and ministers to explain the “truth”.
I would respectfully submit that, as in my own case, too few Christians afford any time to think through the awfulness of an eternal hell - the unspeakable pain and suffering of mind and body, not for a mere 70 years more or less, but for ever and ever and ever. And not only for those who we may think deserve the sufferings of hell, but for all - no matter how kindly and considerately they may have treated others in this life.
This may sound uncharitable, but I’ll ask the question anyway. Do such believers really believe that the vast majority of souls since the Fall, will end up in the agony of hell with no way out - including young children, the aged and infirm; and including those who never heard the gospel but lived their lives according to the light they had.
Calvinists believe that all the non-elect, including non-elect infants, are destined for hell. How can that be just? Arminians believe the same although they explain it differently.
I think a changing point in my experience occurred when I asked myself a question. Could I set fire deliberately to any other living creature, let alone a human being made in the image of God? My answer was no, I don’t think I could. I don’t think that the God who loved us so much that He sent His Son to be the Saviour of the World, i.e. everybody not just a select few, would do what I couldn’t do. I hope that isn’t blasphemy. After all, God is LOVE