The Old Covenant couldn’t have ended at the cross if the apostles were still utilizing it to bring some of the Jews to salvation under the New Covenant. That obsolete, decaying Old Covenant still served a purpose until the generation of Jews who had to transition to the New Covenant ended. I don’t know why it’s so difficult to simply agree with that.
The old covenant absolutely ended at the cross. The new covenant undeniably was established at the cross and it's ridiculous to think that both covenants would be in effect at the same time. No, the new covenant replaced the old covenant immediately when it was established by the blood of Christ (Hebrews 8:6-7, Hebrews 10:9-10).
You clearly don't even know what the word "obsolete" means. The old covenant being obsolete means that it was no longer in effect. No longer valid. Kaput. Done. Finished. Replaced by the new covenant. The tearing of the veil of the temple when Jesus died signified that the old covenant was made obsolete and put to an end and was replaced by the new covenant that was established by the blood of Christ.
Jesus nailed the old covenant and its "handwriting of ordinances that was against us" to the cross.
Colossians 2:13 And you, being dead in your trespasses and the uncircumcision of your flesh, He has made alive together with Him, having forgiven you all trespasses, 14
having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross.
Scripture is clear that the establishment of the new covenant replaced the old covenant, so how could the old covenant still be in force when it had been replaced? That's not possible.
Hebrews 8:6 But now He has obtained a more excellent ministry, inasmuch as
He is also Mediator of a better covenant, which was established on better promises. 7 For if that first covenant had been faultless, then no place would have been sought for a second.
Hebrews 10:8 Previously saying, “Sacrifice and offering, burnt offerings, and
offerings for sin You did not desire, nor had pleasure
in them” (which are offered according to the law), 9 then He said, “Behold, I have come to do Your will, O God.”
He takes away the first that He may establish the second. 10 By that will we have been sanctified through the offering of the body of Jesus Christ once for all.
Notice in Hebrews 8:6-7 above that the second, new covenant was established on better promises than the first, old covenant. Then notice that Hebrews 10:9 indicates that Jesus took away the first, old covenant in order to establish the second, new covenant. This shows that the establishment of the new covenant by way of His death also did away with the old covenant.