Iversen's fledgling career began in his native Denmark with Esbjerg. Former Miller Kari Arnason also had a brief stint at the Danish Superliga side back in 2009. During Iversen's time at the club, Ebsjerg were mostly stuck in mid-table in Denmark's top division. They suffered relegation to the Danish 2nd tier in 2016/17, but they earned promotion back to the top tier at their first attempt. In their Danish Superliga return season in 2018/19, they had their best league finish since 2003/04. Ebsjerg ended up 3rd just behind Copenhagen and Midtjylland, which earned them a place in the Europa League Second Qualifying Round.