At the end of the rosary we pray
“Oh God whose only begotten Son by His life death and resurrection has purchased for us the rewards of eternal life…”
Are you asking whether He atoned for us and for His own death?
If so, in what sense, and what scripture etc. supports this idea?
If I understood you correctly, no. That isn’t what that means.
Let me rephrase and see if I can get a better understanding:
Did Christ’s life and/or his suffering during his life make atonement for us
Yes. It is by one specific aspect of his birth and life that He atoned to Father for our sins. His obedience.
Hebrews 5:7 Who in the days of his flesh, when he had offered up prayers and supplications with strong crying and tears unto him that was able to save him from death, and was heard in that he feared; 8 Though he were a Son, yet learned he obedience by the things which he suffered; 9 And being made perfect, he became the author of eternal salvation unto all them that obey him;
He was obedient unto death.
Philippians 2:8 he humbled himself
and became obedient to the point of death—
even death on a cross.
According to Scripture, God took on the body of a man in order to be capable of death and thus bring about the fulfillment of the Old Testament promises.
Hebrews 9:15 For this reason he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, because a death has occurred that redeems them from the transgressions under the first covenant.[a] 16 Where a will
is involved, the death of the one who made it must be established. 17 For a will[c] takes effect only at death, since it is not in force as long as the one who made it is alive.
And it is by His resurrection that He established the New Covenant.
2 Corinthians 5:14 For the love of Christ urges us on, because we are convinced that one has died for all; therefore all have died. 15 And he died for all, so that those who live might live no longer for themselves, but for him who died and was raised for them.
Anyway, that’s the way I understand it.