One who would be extremely uncomfortable immersing in front of others may he immerse in the middle of the night on Erev Shabbes, Rosh Hashana, Yom Kippur or Yom Tov when the Mikvah is for sure empty?

As mentioned in a previous answer already, if the Tevila can’t be made on Erev Shabbos or Yom Tov day, in need it can be done on the previous night.