Chances are there may be an accident in the crate, but it will be so much easier to clean up than the floor!
I keep the crate beside my bed at night so they aren't suddenly, for the first time in their life ALONE after being removed from their mom/littermates. I also set the alarm for whatever the middle of my sleep night is (2 am?). When it goes off, I quietly scoop up the puppy from the crate, carry it outside to the poo/pee spot. Calmly encourage the poop/peeing (usually just a pee late at night) then quietly go back in the house, toss a treat in the crate for the pup (pup should follow) then back to sleep for the remainder of the night.
MACH3 Bretta Lee Wildhaus MXG MJG MXF MFB TQX HIT CGC TC
Glory B Wildhaus AX, AXJ, XF
"Behind every great man is a woman rolling her eyes." - Jim Carrey