No birth year is recorded anywhere, and the received death year rests on hagiographical sources written centuries after the life. Nobody argues for a particular birth year, because there is no evidence to argue from; the reference literature simply omits it.
What would resolve this A twelfth or thirteenth century document, endowment record or inscription from Yasi, Sayram or Bukhara that names him with a date.
OpenCentral Asian documentary history and Persian hagiographyP. Bearman, Th. Bianquis, C. E. Bosworth, E. van Donzel and W. P. Heinrichs (eds.), The Encyclopaedia of Islam, 2nd edition