No, God could not forgive us without sacrificing his son, because it was written that this MUST HAPPEN, because we were "dead in our trespasses and sins" (Ephesians 2:1).
But God "even when we were dead in sins, hath quickened us together with Christ; by grace you have been saved" (Ephesians 2:5).
And regarding what you say that God could forgive humanity without sacrificing Jesus... that was not possible, because we were "falling short of the glory of God" (Romans 3:23)
God loved us so much that he sent his son into the world to fulfill the Law, and die on the cross, and thus reconcile us with Him.
"For by works of the law shall no flesh be justified in his sight; for by the law is the knowledge of sin." (Romans 3:20)
Jesus, once he fulfilled the law, abolished it, and in this way, he gave us the opportunity to reconcile with the Father, but only if we believe the text of Romans 10:9, and put it into practice.
"That if you confess with your mouth the Lord Jesus, and believe in your heart that God raised him from the dead, you will be saved."
P.S I don't speak English, I use a translator to talk to you, I'm from Argentina and I speak Spanish