As discussed in this question, as far back as the 1960s it was suggested that the Schwarzschild metric can be smoothly joined to a de Sitter metric. For example the idea has been used by Lee Smolin in his ideas idea for black hole evolution.
If the suggestion is true it means that matter falling into a black hole would emerge into a de Sitter spacetime arguably comparable to our own.
So has the universe we live in started as a black hole of this type?
Is it possible to prove that the big bang was a black hole of this type?