IOW, why look to the New Testament, which didn't exist as such at the time? Tanakh is sufficient? Is that why so many Protestants seem not to accept so much of the Gospels?
The problem is protestants accept too much of Rome’s gospel..
But scripture warned us about another Jesus and another gospel..
And Rome has both..
Obviously, much of what was to become the New Testament was already extant when Paul penned those words. The writings were widely-distributed and known in the early church.
The books of the Old Testament imply their own insufficiency. How could someone read the OT and not realize that it is incomplete? It all points to God's Messiah who had not yet come. It is a prophesy awaiting fulfillment. Clearly, the rest of the story was waiting to be written.
Protestants do not accept much of the New Testament? Pretty broad brush you're painting with. Faithful Protestants might not accept the fanciful Catholic interpretations of the four Gospels but that is a long ways from saying that they have rejected those texts.