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Pope Pius IX, in his dogmatic definition of the Immaculate Conception, Ineffabilis Deus, stated that the Blessed Virgin Mother's soul was free from original sin
in primo instanti creationis atque infusionis in corpus
in the first instant of [its] creation and infusion into (union with) the body
"Creation" and "infusion" are simultaneous.
"Instanti" here is the singular ablative of "insto" (instant); there is one instant (not one for creation and another for infusion
This is St. Thomas's teaching, too (Summa Theologia I q. 118 a. 3 co.):
we must simply confess that souls were not created before bodies, but are created at the same time as they are infused into them.
simpliciter confitendum est quod animæ non sunt creatæ ante corpora, sed simul creantur cum corporibus infunduntur.
Thus, since there is no duration of time between the soul's creation and union with the body, there is no immaculate soul first and later, once united to the body, a soul stained by original sin.
This doesn't mean God taints the soul with original sin when He creates it, though; God is not a cause of sin.