What happened the moment Jesus died on the cross, is very vividly stated in Matthew 27, verse 51:
"At that moment [that was the moment that Jesus died] the curtain of the temple was torn in two from top to bottom." (NIV)
What did that curtain of the temple represent? It represented the separation between a holy God and sinful man. But through the death of Jesus, because He bore our rejection, He obtained for us, acceptance and the evidence of acceptance was the splitting of that curtain, and it was split, the Scripture carefully says, from top to bottom. It was done not by man, but by God. Jesus had endured our rejection that we might enter into His acceptance.
Now this acceptance through the death of Jesus is described by Paul in various places, especially Ephesians, chapter 1, verses 4 through 8, where he says this:
"For God chose us in Him [that's in Jesus] before the creation of the world to be holy and blameless in his sight. [Isn't that beautiful to be holy and blameless in God's sight. How could we ever achieve that by our own effort? It's not possible by anything but through the substitutionary death of Jesus] In love God predestined us to be adopted as his sons through Jesus Christ, in accordance with his pleasure and will. [Note, we're to be sons, we're to be children. We're not aliens or strangers. We're members of the Family. God is our Father, Heaven is our home, we belong to the best Family in the universe. Paul continues] to the praise of his glorious grace which he has freely given us in the One he loves." (NIV)
I always like the King James Version of that verse, it says, “God has made us accepted in the Beloved”. There's the exact translation, from rejection to acceptance as God's children, members of His family. Verse 7, Paul goes on:
"In him [Jesus] we have redemption through his blood, the forgiveness of sins, in accordance with the riches of God's grace that he lavished on us with all wisdom and understanding." (NIV)
Notice the emphasis on grace. It cannot be earned. We have redemption through His blood, we are redeemed from the curse to enjoy the blessing; redeemed from rejection to enjoy acceptance. We are not ‘far away’ anymore, but we are now ‘near’, to freely live in the presence of God the Father.
Dear Father, I’m so glad I can now freely come into Your presence, in Your beloved Son Jesus. Thank You that I don’t need to carefully tread, that I don’t need to be afraid You would reject me, or that perhaps You don’t listen to me, but that I can now always have Your full attention, that You fully love me, that I am completely accepted. I praise You, I love You, I thank You! In Jesus’ wonderful Name, Amen!