If you don't trust them, you can compile it on your own.
I don't really know much about how Brave is made, but you make it sound like they're using proprietary Google libraries, whereas I was under the impression that it was built from open-source software. If I'm right, the fact that this software originally came from Google is immaterial. If it's open source, Brave have full control over what it does and Google has zero.
Brave uses Chromium: an open source project controlled by Google. They can submit patches back to Google, but if Google don’t want to take them they don’t have to integrate them. So that leaves Brave with three options: they can take Google’s Chromium as is and focus on the browser interface potentially flipping a few config switches, they can maintain their own set of patches and update over time, or they can fork and go it alone. So far they’re hovering between options one and two. The closer they get to three the less influence Google has but the more it costs Brave. At the moment they’re not being particularly courageous with reducing their Google alignment.