Do you have any pinging or clicking sound when tuning up? Is it all the strings, or just a few strings? You said it’s a new guitar. Are you sure the correct gauge strings are on there?
You could take 1500 grit wet dry sandpaper, fold it around a thinner guitar string than the nut slot you are going to sand and with very light pressure, make a few passes in each slot to smooth out the bottoms of the nut slots. You do not want to make the slot any wider/ deeper so go slow and keep checking before doing more.