I know I'm late to the party on this one but the answer may be helpful for someone searching with a similar question.
It's very, very simple. When a PC or laptop manufacturer or vendor says they don't support Linux, what they really mean is, "We don't know how to use Linux so don't ask us any questions." In short, they are saying, "DUH! Linux? We only hire Windwoes Drones"
Now, there are two things you can do to circumvent the issue.
First, go to your preferred retail store with a Linux USB flash drive and either insist on testing it or get a commitment from the salesperson that you can return the machine if Linux doesn't work, which is highly unlikely unless you are buying some over-done trash like a Mint Box or other custom designed machine.
Second, the G513 is user-upgradeable so buy a separate NVMe device, remove the one supplied by the manufacturer and replace it with your newly purchased NVMe. Install Linux and pack the original NVMe away. If you ever have to make a warranty claim, simply put the original NVMe back in (it has Windwoes on it), and you're good to go.
As for the G513, and almost all brand name laptops, they run Linux fine.
In summary, "We don't support Linux" is industry code for "Que?"