For AMD, support varies. Ubuntu LTS versions ought to have good support, but switching to a non-LTS version or a different distro is harder, as you may have to recompile the drivers yourself.
Due to a few posts elsewhere (people doing Tensorflow and such), I thought that Ubuntu 18.04 LTS did have Quadro P400 support via the proprietary drivers. It could also mean your EFI BIOS (motherboard) is one of the "uh-nuh, I don't like Linux" versions, with incorrect ACPI tables and whatnot that their Windows drivers just ignore.
Keeping strictly to the latest Ubuntu LTS version, and upgrading the Nvidia proprietary drivers whenever released) would be the only way I would use it, if I had to do some Cuda stuff, so if the Live DVD wasn't the 18.04 LTS version, you could give that a try. Any other distro versions are iffy, because Nvidia drivers are binaries, and tend to only work well with a specific kernel version. (So, trying say Ubuntu 19.10 tells you nothing about how the Nvidia drivers work in 18.04 LTS.)
I am hesitant to suggest using Linux on that hardware, though, because I only run Linux on hardware that has no gotchas or proprietary drivers. I want my tools to work well, so I tend to pick the hardware I know works with Linux.
I used to have an AMD 780G a decade ago that worked better with the proprietary drivers, but they were nasty enough (overwriting Mesa stuff etc.) that I switched to the then slower/less efficient, beta-quality open-source drivers, and kept updating at least once a month, just to avoid crashes. Nowadays, the x86-based machines I have all have Intel integrated graphics (this laptop here has Intel HD 620), so I have no first-hand experience on the current state of either the original open-source drivers for AMD, nor the state of the now-opensourced AMD "proprietary" drivers.
Testing with a Live DVD/USB stick/SSD via USB3 is the only way to be sure.