Hiccups and no burps

My son is 6 days old and I'm exclusively breastfeeding. I know that burps are fewer if you BF but I can't ever get him to burp. I've tried the three main holds, over shoulder, sitting cupping his chin, and laying flat cupping his chin. He tends to get hiccups a lot and I'm assuming there's a correlation to his nonburping?  He doesn't spit up so that's one positive. Any mom's with any tips to get him to burp and stop the hiccups from one exhausted mom to another?  Thanks!!!!