I stayed up all night until sometime near noon the next day.

The word sometime is an adverb, but can I use it, as a noun, like above?.
Or should sometime be the two -word phrase some time?

sometime adverb at some not specified or definitely known point of time <sometime last night> [m-w.com]

It's an adverb, not a noun, in your example.
sometime near noon, sometime last night, sometime tomorrow, sometime last week, etc.
I get how the adverb someitme works!
Thanks, CJ.