I'm sorry, but this is not necessary at all. Chr*stianity bases its claims and those of the "new testament" on being somehow "authorized by," "prophesied by," or a "fulfillment of" the "old testament." If the "old testament" does not authorize or prophesy the "new," then chr*stianity falls flat. Otherwise, the "new testament" would have been added to the Jewish Bible to form a single sacred book, but would have been completely separate, like the so-called "holy qur'an."
The ancient sacrifices were mitzvot--commandments. Those of Yom Kippur were specifically for the sins of Israel. Likewise, the individual Israelite brought sacrifices for certain unintentional sins. For intentional sins, only teshuvah (repentance) obtains forgiveness. This has always been the case, whether or not the Temple was standing.
The Temple was destroyed once before by the Babylonians. The Jews had no access to sacrifices for seventy years, yet the Messiah hadn't come. The exile of the past two millenia differs only in quantity, not quality. Furthermore, the Torah clearly prophesies in both Leviticus and Deuteronomy that Israel would be exiled from its Land. Exile, by definition, meant no access to the Temple and its service. The Torah states quite plainly that this will come about as a punishment for the sin of forsaking the Torah. It never so much as intimates that Israel will be punished for "rejecting the Messiah" or holding onto the Torah after it has allegedly been "fulfilled."
As to law and good works, until the reformation of Martin Luther chr*stians spent fifteen hundred years meriting salvation via law, good works, rituals, and sacramental confessions. This being the case, one can only wonder why a new religion was ever necessary.
When exactly did the OT books get codified as being scripture, was it before or after Christianity?
I'm sorry, but this is not necessary at all.
If I didn't know better...I'd suspect people who cannot read Christian scripture--even to debate it-- were merely afraid to read what Jewish eye-witnesses to Jesus' resurrection wrote in the New Testament--as it might shake their self-righteous delusions. Go ahead, rely on your own law-keeping, and see where it will get you.
"The Holy Spirit spoke the truth to your forefathers when he said through Isaiah the prophet:
26" 'Go to this people and say,
"You will be ever hearing but never understanding;
you will be ever seeing but never perceiving."
27For this people's heart has become calloused;
they hardly hear with their ears,
and they have closed their eyes. Otherwise they might see with their eyes,
hear with their ears,
understand with their hearts
and turn, and I would heal them.'
28"Therefore I want you to know that God's salvation has been sent to the Gentiles, and they will listen!"
(New Covenant book of Acts 28:25-28)