Is it normal for a new motherboard to be missing CPU mounting brackets?

I wouldn’t worry too much; if the backplate is still there, you might be fine without those brackets. Just keep in mind that resale later could be trickier without them. Still, if you bought it new, definitely consider exchanging it just to be safe.

This isn't normal. Some coolers do need you to remove the brackets, but most require them. I'd recommend contacting the retailer for an exchange. Better to be safe than sorry!

Missing mounting brackets is definitely not normal! You might want to check with the store where you bought it. They should help you get a new board since it shouldn't have arrived like that.

It sounds like you might have ended up with a used board. Could be that the previous owner had an aftermarket cooler and forgot to put the brackets back before selling it. But definitely check the store for a replacement!