Do we become saints at baptism?

At Mass this morning our priest told us that we become saints when we are baptised. Is this correct?

In the sacrament of baptism (Catechism no. 1263), “all sins are forgiven, original sin and all personal sins, as well as all punishment for sin. In those who have been reborn nothing remains that would impede their entry into the Kingdom of God, neither Adam’s sin, nor personal sin, nor the consequences of sin, the gravest of which is separation from God” (Note: infants are forgiven original sin). After making our profession of faith while receiving the holy Baptism that cleansed us, we are pure and spotless like the saints in heaven. If one were to die immediately after baptism, he would go directly to heaven.

When we made our first profession of faith while receiving the holy Baptism that cleansed us, the forgiveness we received then was so full and complete that there remained in us absolutely nothing left to efface, neither original sin nor offenses committed by our own will, nor was there left any penalty to suffer in order to expiate them” (Catechism 978). At that moment the newly baptized are pure and spotless like the saints in heaven. If one were to die immediately after baptism, he would go directly to heaven. “Yet the grace of Baptism delivers no one from all the weakness of nature. On the contrary, we must still combat the movements of concupiscence that never cease leading us into evil " (ibid. 978)

However, for the newly baptized who remain on earth , the battle against sin continues.
“Certain temporal consequences of sin remain in the baptized, such as suffering, illness, death, and such frailties inherent in life as weaknesses of character, and so on, as well as an inclination to sin that Tradition calls concupiscence, or metaphorically, “the tinder for sin” (fomes peccati); since concupiscence “is left for us to wrestle with, it cannot harm those who do not consent but manfully resist it by the grace of Jesus Christ.”
(Catechism no. 1264)

“In this battle against our inclination towards evil, who could be brave and watchful enough to escape every wound of sin? “If the Church has the power to forgive sins, then Baptism cannot be her only means of using the keys of the Kingdom of heaven received from Jesus Christ. The Church must be able to forgive all penitents their offenses, even if they should sin until the last moment of their lives.” (*Catechism * no. 979)

“It is through the sacrament of Penance that the baptized can be reconciled with God and with the Church:

Penance has rightly been called by the holy Fathers “a laborious kind of baptism.” This sacrament of Penance is necessary for salvation for those who have fallen after Baptism, just as Baptism is necessary for salvation for those who have not yet been reborn (Catechism 980).

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