You should worry about newborn hiccups when the newborn has other signs like being really fussy or if they are arching their back a lot during feeding or after feeding.
Newborn hiccups are usually nothing to worry about and not often a cause for any concern even if the newborns hiccups last longer than 10 minutes or longer.
Although if the hiccups persists longer than 30 minutes to an hour you may want to contact the pediatrician or take them to urgent care if they are having other issues.
Unless the hiccups interfere with the baby's eating or sleeping then there's no real need to see a doctor unless they are really in distress.
Most hiccups will go away even in newborns, just like they do in older kids and adults.
In some cases burping your newborn or baby when they have the hiccups may help to get rid of the hiccups.
Burping your baby is also important after feeding a newborn and can help get rid of excess gas buildup which might be causing the hiccups.
If you breastfeed your baby, you should burp your baby before they switch to a different breast and rub or gently pat your baby's back when they do have the hiccups.