“Ado” means agitation or fuss. It generally has negative connotations. So “without further ado” means “without any more fuss” i.e. “let’s get on to the main event.”
If you were to be saying/doing something else first, you’d be more likely to say something like “But before we get to that…” In this way, you’re acknowledging that the main thing is yet to come, but you’re not discrediting or downplaying what you’re about to say/do.
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