Is it possible to control new window position of Brave Browser?

This may be a bit of an over-engineered solution, but you could use an app like Keyboard Maestro (or something else similar). Create a macro that will open a new window at a certain position on the screen. Then, in System Preferences -> Keyboard -> Shortcuts -> App Shortcuts change the "New Window" menu item to a different keyboard shortcut and set your other macro to trigger with ⌘N. This way, you don't have to change your behavior at all, but a new Brave window will open exactly where you want it. I'm sure there is other window management software that will do something similar.