WARNING: Some users reported higher power usage after running this as well as HDMI issues resuming from suspend. This also assumes it's the nvidia card that's running your HDMI. I can not test this myself. Users reading this should not attempt this fix just because their HDMI sound isn't working as it's explicitly for the OP who doesn't have HDMI sound detected at all.
1. Download this file and extract it's contents. Everything that follows is done in the terminal.
2. Change to the directory where you extracted the files, eg.
cd Downloads
3.
make
4.
sudo make install
5.
echo nvhda | sudo tee -a /etc/initramfs-tools/modules
6.
echo "options nvhda load_state=1" | sudo tee /etc/modprobe.d/nvhda.conf
7.
sudo update-initramfs -u
8. Now reboot your computer.
I do think this will work for you, and I hope it doesn't cause any new issues. There was a completely successful use of this by a person running 18.2 and I see no reason for it to not work on 19. Here is a link to their post: https://bugs.freedesktop.org/show_bug.cgi?id=75985#c33
You may have to use pavucontrol after the reboot to adjust settings, but even that might not be necessary.
Good luck.