There are historical documents from the classical period that are about the pronunciation of latin. Ecclesiastical Latin is church Latin, hence the name, and Classical Latin is how it was (generally) spoken around the time of the texts.

A very easy example to point to is Ceasar being pronounced See-Zar like the salad or Kai-Zar. First is church approved latin and the second is classical.

Here's a couple videos by an Italian Linguist (english, italian, japanese, latin) who also does a lot of history content using primary sources that he can read.

https://youtu.be/x6Fg3RcYKJI differences between the types of latin

https://youtu.be/YlggQMFPjKw reviewing the latin used in Barbarians on Netflix.