FWIW, I looked a bit more into it and it seems this "blank screen with audio" is a known Nvidia-related issue, which is usually solved by selecting "Let the 3D application decide" and/or turning off "Antialiasing - mode" in the Nvidia control panel. It apparently clashes with the Godot "viewport" or something. That said, this still didn't do anything for me, no matter how I fiddled with it.
I should also mention there is a Godot game which does work for me, "Megaman Rock'n Roll". It is built on Godot 2.1, whereas this is 3.5.3 (?), which might shed light on the problem. I've also seen mention of switching from GLES3 to GLES2 solving the problem.
edit: "The Legend of Lumina" also works, despite using also 3.5.3 (?)