Non burping newborn

Has anyone dealt with a newborn who doesn't burp?!! My son is a week old today and every time we try and feed him after eating he never burps! I've tried the over shoulder, the knees, and sitting him up position and nothing! I even rub his back in between trying. I'm using Dr brown bottles and it says it helps prevents burps but I didn't think it would cause baby not to burp at all? And it causes him to spit up or get the hiccups. Advice?