In the beginning, Aule the Smith created the Seven Dwarf Fathers and six wives.
Durin the Deathless was the only one without a wife, so how did his bloodline begin?
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As discussed here, one was created alone (Durin), then the other six fathers of the Dwarf race and their respective spouses.
Per Tolkien's own Letter #212, we know that there were created...
"One, the eldest, alone, and six more with six mates".
From The Hobbit are also derived the matter of the Dwarves, Durin their prime ancestor, and Moria; and Elrond.
That being the case, there doesn't seem to be any special reason to assume that Durin didn't marry one of the children of the other Dwarf fathers once they'd come of age. Dwarves are known to be long-lived and marrying the Elder Dwarf would presumably be an honour for the family of whichever dwarf lady he managed to secure as his wife.
We do know that Durin was unequivocably the progenitor of the Dwarf race, whom all other dwarves relate to, even those that also relate to one of the six fathers. so there must have been a reasonable level of interbreeding in the earliest days of the race.