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But is there proof that such a dimension exist?

No, there is not. But its existence can be inferred. If there is a dimension where time and space do operate and there is such a dimension – the world we experience, then we can infer that there is a dimension where time and space do not operate – Nirvana. Again, even though we cannot prove Nirvana exists, we have the Buddha’s word that it does exist. He tells us:
“There is an unborn, a not-become, a not- made, a not-compounded. If there were not, this unborn, not-made, not-compounded, there could not be made any escape from what is born, become, made, and compounded. Therefore is there made known an escape from what is born, made, and compounded.”

Ud 80

We will know it when we attain it. Until that time, we can practise.