Though I once worked for a whitebox PC manufacturer, I wasn't directly involved in the production side and instead was responsible for network management on the business side of the organization. This was also in the late 1990's to early 2000's period, so the BIOS and versions of Windows have changed drastically since that time.
That's why I still recommend you go to the HP forums and post your questions there, since they should know their devices and have people there better than anyone here who might be able to answer your questions.
However, I will provide the following entry point into the Windows 10 documentation related to booting and installing Windows, since these should cover the processes that are occurring when you restart the PC with a wiped drive as you've apparently been doing.
Boot and install Windows | Microsoft Docs
Note that the URL I provided takes you directly to the Boot and install Windows section, which is likely what's been happening to you and why you can't seem to stop this. However, if you look at the left hand pane, you'll notice it's a table of contents that also includes other boot options like Boot to UEFI Mode or legacy BIOS mode, which I believe is what must be used to install alternative operating systems.
My knowledge of any of this including installing Linux or other operating systems is limited, since I've never done it myself and only read about it or seen it mentioned in forum posts, which is why I keep telling you to look elsewhere for this aid. I'm sure there are others here who might know, but the title of your thread "Trusted installer" and the way the thread progressed with discussions of a Trojan in a forum relating to viruses and malware aren't likely to result in the people who might be able to help ever finding your true question to offer their aid.
That's why I recommend you start over, preferably in the HP forums or at least in a more appropriate forum here that has nothing to do with viruses or Trojans and begin a new thread, titling it with what you're actually trying to do rather than some random issue you're having.
These are the reasons no one before me could answer any of your questions, since they were incoherent and confused, so the answers were as well.
Rob