No, because God creates the soul immediately and unites it immediately to the matter when the matter is properly disposed.

The soul is the substantial form of a human, and the form+matter of something cannot exist apart from one another.

^{Even death, when the soul separates from the body (i.e., no longer animates it), does not sever the relation the body and soul have to one another; hence why our bodies will resurrect on the last day.}

St. Thomas Aquinas, Summa contra gentiles ch. 89, n. 17 (cf. Compendium Theologiæ ch. 95 on the soul's "immediate creation by God"):

when the body is actually human, as being perfected by the human soul, it neither precedes nor follows the soul, but is simultaneous with it.
_{Cum vero est humanum actu, quasi per animam humanam perfectum, non est prius neque posterius anima, sed simul cum ea.}

This truth seems implicitly contained in Pope Pius IX's declaration of the dogma of the Immaculate Conception, Ineffabilis Deus, where he says:

the most Blessed Virgin Mary, in the first instance of her conception (primo instanti suæ conceptionis)

He does not say "her soul's" nor "her body's" but "her [body+soul composite] conception", i.e., the conception of her person.

^{cf. "Could 'The human soul is created at the moment of conception.' be defined as dogma?"}

Creation & infusion one simultaneous act

No, because God creates the soul immediately and unites it immediately to the matter when the matter is properly disposed.

The soul is the substantial form of a human, and the form+matter of something cannot exist apart from one another.

^{Even death, when the soul separates from the body (i.e., no longer animates it), does not sever the relation the body and soul have to one another; hence why our bodies will resurrect on the last day.}

St. Thomas Aquinas, Summa contra gentiles ch. 89, n. 17 (cf. Compendium Theologiæ ch. 95 on the soul's "immediate creation by God"):

when the body is actually human, as being perfected by the human soul, it neither precedes nor follows the soul, but is simultaneous with it.
_{Cum vero est humanum actu, quasi per animam humanam perfectum, non est prius neque posterius anima, sed simul cum ea.}

This truth seems implicitly contained in Pope Pius IX's declaration of the dogma of the Immaculate Conception, Ineffabilis Deus, where he says:

the most Blessed Virgin Mary, in the first instance of her conception (primo instanti suæ conceptionis)

He does not say "her soul's" nor "her body's" but "her [body+soul composite] conception", i.e., the conception of her person.

^{cf. "Could 'The human soul is created at the moment of conception.' be defined as dogma?"}

The creation of the soul and its infusion is one instantaneous act. We can distinguish them in our minds (logical distinction), but they can't exist separately in reality. A human soul with no relation to a human body makes no sense because the soul is the substantial form of the body.

Pre-existentianism

Pre-existentianism is the heresy that human souls exist before the creation of their corresponding bodies. It was condemned in the Canons against Origen (Denzinger 203):

1. If anyone says or holds that the souls of men pre-existed, as if they were formerly minds and holy powers, but having received a surfeit of beholding the Divinity, and having turned towards the worse, and on this account having shuddered (apopsycheisas) at the love of God, in consequence being called souls (psychae) and being sent down into bodies for the sake of punishment, let him be anathema.

and the Council of Braga against the Priscillianists (Denzinger 236):

6. If anyone says that human souls first sinned in the heavenly habitation and in view of this were hurled down into human bodies on earth, as Priscillian has affirmed, let him be anathema.

^{source: Ludwig Ott, Fundamentals of Catholic Dogma, bk. 2, § 15. The Origin of Individual Human Souls, p. 99}