Baby coming sooner than planned....

Anyone with their first pregnancy have their baby come early? I dont mean like needed a c-section or to be induced, I mean like you were 36+ weeks and baby came naturally. I'm not due until Jan 16th but everyone on both sides of the family feels like she will be coming early. I'm saying New Years, my husband thinks Christmas lol, and his aunt thinks between Christmas and New Years. Is it possible that she may come early like that, naturally?? **I did go to L&D last week because I was feeling super crummy and was having somewhat consistent contractions, but I wasn't feeling them or progressing at all (I'm 31+4)