I almost never print cut sheet, but with rolls, it's the same. Rattle, click, whir, finishing...
I find that if I'm in a hurry, the printer will then decide to do a nozzlle check.
Only thing that seems to speed it up is if I turn on auto cut, which is fine for prionting cad plans, but not what I want with a decent print, and not even vaguely related to your use case.