But first, this was only for Israel. We know that gentiles could also repent and be forgiven (the Ninevites, for example).
Second, we can see from the Hebrew scriptures that God can forgive sin even without the Levitical sacrifices. Does God desire sacrifice?
Third, even assuming the divine inspiration of the gospel, does this invalidate God's promises from the Hebrew scriptures?
I will lift up the cup of salvation
and call on the name of (Psalm 116:13)
And it shall come to pass that all who call upon the name of shall be delivered (Joel 2:32)
Gentiles were also allowed in, hence the instructions on treating the strangers that sojourned among them. The Ninevites also believed God's word as preached to them by Jonah.
It all comes down to believing what God has said.
Second, we can see from the Hebrew scriptures that God can forgive sin even without the Levitical sacrifices. Does God desire sacrifice?
God desires people to trust Him.
Third, even assuming the divine inspiration of the gospel, does this invalidate God's promises from the Hebrew scriptures?
Invalidate? No, it just changes the basis of belief. In the Hebrew Scriptures God said He would send a Prophet like unto Moses and it was Him to who Israel should listen.
The Christian Scriptures don't say the Israelites were wrong for following the Levitical system. They say the purpose of that system was to bring to our mind the enormity of our sin. Then when we acknowledge our sinfulness we see our need to be reconciled to God and that reconciliation comes through accepting the once for all sacrifice of Jesus of Nazareth, the Jewish Messiah.