Galatians 4 two separate & opposing covenants.

[Guojing]

No

Acts 2:4 Pentecost JEWS ONLY receive the spiritual outpouring baptism of Christ's indwelling Holy Spirit. This is the fulfillment of the Jer & Heb books & exclusive to Israel. The new covenant promise it later expanded in include gentiles.

The promise of salvation is given 1st to the Jew then to the gentile

It's at Cornelius house (Acts 10) several years after the Acts 2 outpouring of the Holy Spirit. Where Gentile's are granted the spiritual baptism of Christ's indwelling Holy Spirit (See Acts 11:16 below).

Acts 10:
44 While Peter yet spake these words, the Holy Ghost fell on all them which heard the word.
(MY NOTE: As Peter is speaking the Holy Spirit indwells the gentile listeners.)

45 And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost.
(MY NOTE: The believing Jews that came with Peter (the Acts 2 Pentecost speaker) are ASTONISHED that God has granted gentiles eternal life)

Peter shares/revisits his Acts 10 experience
Acts 11:
15 And as I began to speak, the Holy Ghost fell on them, as on us at the beginning.
(MY NOTE: Christ baptizes with the Holy Spirit (Matt 3:11) And He fills/baptizes gentiles Acts 10;:4)

16 Then remembered I the word of the Lord, how that he said, John indeed baptized with water; but ye shall be baptized with the Holy Ghost.
(NOTE: Upon returning to Jerusalem Peter explains to the circumcision/Jews that contended with him (Acts 11:2). About Acts 10 gentile receiving of Christ's """baptism with His Holy Spirit""")

If your answer is no, then we cannot accept the New Covenant on their behalf (Hebrews 8:8), so your following note cannot be correct

MY NOTE: New Covenant - ALL the believers sin > Past-Present-Future > Forgiven/Pardoned/Washed Away. NEVER to be remembered)

If you want to follow Hebrews 8:8-12 strictly for us, our sins will only be forgiven when the New Covenant begins with the nation Israel, which cannot be happening now, since the current nation of Israel has fallen (Romans 11:11).

Our salvation is a present one, not thru the New Covenant, but rather because we are in the Body of Christ, which was a mystery unknown in the OT, until Paul.