A kakuja comes from a mutation that happens in the kakuhou after repeat cannibalization leads to high RC concentrations in the body. I assume this mutation is not present in normal ghouls and must be obtained through cannibalization. Ghouls like the Washuu however are born with this mutation already. This does not mean they have a kakuja though, just that they are capable of growing one. This is the same as how a ghoul's regular kagune becomes larger and stronger the more they eat.

Kaneki gets a Washuu's kakuhou, Takizawa and Amon get Owl's kakuhou (which is not Washuu but is a kakuja). We can see neither have full kakujas but we see that within a year of having their kaukuhous all three of them have half kakujas of their own. This is in comparison to someone like Jason, who had a weak half kakuja himself despite cannibalizing for much longer period of time.