I just noticed that you asked about before the Exodus. The rules then were the same. A child of two people was a member of his father's tribe. The inheritance at the entry into the land was based on the entrant's tribe (and from his father). This had nothing to do with "forbidding" a man from one tribe to marry a woman from another.
בְּמִדְבַּר Chapter 36 has the halacha of an heiress (a woman with no brothers whose father dies) being forbidden to marry a man from a different tribe because the children (who would inherit the land of their maternal grandfather) are members of their father's tribe. Thus, the land which should have stayed in the mother's tribe, is now owned by the father's tribe. This applied only to the generation that entered Eretz Yisrael. The halacha was cancelled on the 15th of Av the next generation.
Note that a woman who had brothers was allowed to marry out of the tribe because she would not inherit land from her father. Similarly, a female Levite or the daughter of a Kohen did not have any land to inherit.
Chabad.org explains that on the 15th of Av:
The tribes of Israel were permitted to intermarry. In order to ensure
the orderly division of the Holy Land between the twelve tribes of
Israel, restrictions had been placed on marriages between members of
two different tribes. A woman who had inherited tribal lands from her
father was forbidden to marry out of her tribe, lest her
children—members of their father’s tribe—cause the transfer of land
from one tribe to another by inheriting her estate (as recounted in
Numbers 36). This ordinance was binding on the generation that
conquered and settled the Holy Land; when the restriction was lifted,
on the 15th of Av, the event was considered a cause for celebration