In earlier posts on the Jepsen and Jepson boards, he was said to be from Schleswig-Holstein. It was also mentioned that a brother and sister had also emigrated.
Lack of 1860 and later censuses for that area make research difficult, but I will list this "long shot" from Ancestry:
Name:Hans Kristian Jepsen
Birth Date:3 apr 1867
Cristening Date:14 maj 1867 (14 May 1867)
Christening Place:OSBY, HADERSLEV, DENMARK
Father:Jep Kristensen Jepsen
Mother:Kirstine Marie Hansen
The birth month and day are a close match, the mother was a Hansen, and he may also have been older than he listed in 1900.
But unless names and ages of the siblings who also emigrated can be determined, coincidence can't be ruled out.