In the final arc of Ah! My Goddess, Hild, Urd, Skuld, and the goddess sent to examine Belldandy and Keichi’s love are passing the time while the latter pair are off being tested by the Gate. Said test only starts with walking through an arch, and is much more.. difficult, especially after Bell’s father usurps the test and possesses Gate-sama. (BTW, he’s not Kami-Sama.)
Now bear in mind that the test, as shown in the AMG movie, was not exactly canon. But for the final arc of the manga, the author added a similar process and idea; that the members of two different races, being permitted to marry meant being subjected to a test so difficult that no one EVER succeeded. So from the moment of its introduction in the canonical arc, he had one, tensey-weensy problem to explain.
Urd. Daughter of Hild and an unnamed god. (who, as has been noted, wasn’t Kami-Sama). So how did that happen? As the Goddesses and Hild discuss it, the answer becomes clear: Hild and her paramour took the test, and they, like everyone else, failed. But Hild wouldn’t take no for an answer, and being the ruler of Hel, was powerful enough to force a loophole. She created a spell that broke the system, just for the two of them. Once, just once, she was able to meet her lover again, and conceive Urd. But the price of breaking the rules was draconian. They could only meet once, safely. If she ever meets him again, even by accident, she dies.
A couple of links back to earlier speculation:
Who is Keichi Morisato?
More AMG Manga Reflections
Ah! My Goddess, the Movie