Most definitely not...
Generally speaking, any man or woman thinking about having sex with a partner during their first encounter should always use protection.
As a matter of fact, continue to use protection until y'all both get tested, going raw on the first date is playing with both of y'all's health.
Y'know, how many people have caught HIV, STDs, etc from just that first time? Those few minutes of sexual feelings aren't worth compromising your health and physical/mental well-being, messing around, and you'll be on the edge of your bed a few days or a week later, in pain and/or not feeling well, crying cause you don't know what's going on with you.