Klára Dán was born in Budapest, Hungary, into a well-to-do Jewish family. From a young age, she displayed a keen intellect and a talent for languages and mathematics, setting the stage for her later academic pursuits, although the opportunities for women were limited in that historical period.

Klára obtained a degree in mathematics from the University of Budapest. Details about her life and career during this period are scarce, but it's known that she possessed strong intellectual curiosity and a sociable personality. She worked briefly in insurance before her future marriage altered the trajectory of her life.