No. You are starting with a flawed assumption, and if in fact those books are canon, then you would have had to wait 1577 years after Christ's birth for the first infallible ruling in them at Trent. I suggest the articles here:
Articles | Canon Fodder
Infallible rulings by ecumenical councils normally only occur when a long standing belief has come into question. The first infallible ruling on the Trinity doesn't occur until the 4th century for that reason. A non-Trinitarian will use the same argument you are making to disprove the validity of the Trinity you know. It wasn't ruled infallibly until the 4th century, so therefore it was made up in the 4th century and not true. Instead of the fact that people were beginning to teach that Christ was not God, leading the Church to formalize the dogma of the Trinity in response.
The reality is the first attempt by the Church to officially canonize the Scripture (both Old and New Testaments) occurs at the Councils of Carthage and Hippo in the 4th century and is accepted by Pope Damascus. That canon includes those books. Compare the list between those councils and Trent. It's the exact same list of books. Those councils are also the first official canonization of the NT, resolving several disputed books. Those books are included in the Latin Vulgate and in the canon down through the centuries. They're in the first printing of the Bible in Gutenberg. They're in the original KJV. And then they're removed.
All the Council of Trent did was affirm the same books that were in place from the very first canonization of Scripture from those local councils. Why? Because Protestants were removing books from the originally accepted canon of the Church. Just like people were denying that Christ was not God, requiring a formal council to declare the truth of the Trinity in the 4th century. It's the same game.
Those books are also in the canon of the Ethiopian Jews, who migrated to Ethiopia a few centuries before Christ was born. So the idea that they were never in any Jewish canon is false.
However, Jews do remove them from their canon in the 1st century. They also reject the Gospels as being canonical Scripture at the same time.
So, who has the authority to determine which books are valid in your view? A Jewish council or school which rejects the validity of the Gospels, or a Christian council that correctly canonizes the New Testament?
I can tell you who it's not. It's not people 2000 years later on the internet trying to prove or disprove references between the books.
And my original point remains. Those books are in every official canon of Scripture that begins in the 4th century. So yes, if you believe they don't belong, then Christianity had to wait 1600 years before having a correct Bible. Try to explain that to someone you want to convince the Bible is inspired and inerrant, assuming they have done their homework of course.