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Experimental status of the Big Bang theory

I'm aware that the Big Bang theory have unanswered questions related to the very first moments of the Big Bang.

I also know that for our current Universe state, the Big Bang theory with the Inflation theory have great success with respect to many observations like the homogeneity, CMB etc.

My question is, for our current Universe state, is there any observation(s) which could not be justified by the Big Bang theory?