Much of the counterpoints have already been made in the comments. Allow me to make a few points.

 1. Arguments from silence, especially in regard to the Biblical text or other ancient texts, fail because they don’t realize that the author has very specific intentions when he is writing, and certain events may be left out because the author doesn’t see the relevance in the event. One could counter this by saying the author of Acts would most certainly want to record debates over the Trinity, but that’s not something that can be proven. It’s just an assertion. One could also argue that he did record it, but the documents have been lost to history. Either way, it’s an argument from silence. 
 2. Regardless of the lack of specific mentions of Trinity debates, there are mentions of disputes between the Jews and Christians. It’s entirely possible that these debates included trinitarian debates. Along with that, Luke does record the Pharisees objection to Jesus when they say he “makes himself to be God”.