Did the Church determine the canon of the Bible, or discover it through evidence?

It is both. This is the controversy between presuppositional and evidential apologetics, and one cannot really do without the other. On the evidence side, God has never put his servants in the position of just dreaming up a position; he made us intelligent and expects us to gather a lot of evidence: who wrote the book, whether there is anything heretical in it, whether it agrees with the other inspired books, whether it comes from the proper time and source, and so on. On the presuppositional side, there are certain truths God has already given us; he says he has placed his laws on our hearts. So with the canon, both take place, presupposing and gathering evidence to back it up. That is how the church did it, and then she has the guarantee of the pope, because Jesus said whatever you bind will be bound in heaven. The Council of Trent is the first time we have an official, infallible statement on the canon, but Trent did not reinvestigate everything; it went back to the earlier councils, Rome, Carthage, and Florence, which all agreed on the seventy-three books, and put its stamp of approval on it. All those councils were guided by the Holy Spirit, but legally you need at least one definitive statement to make it infallible and irreformable, and that is what Trent did.