When you plug in the USB stick and power up the machine, do you briefly see a Grub Menu upon powerup?
If so, tap the e key.
You should see a grub file screen that is similar to this:
I stole that image from elsewhere on the web.
You see where it says quiet and splash... add nomodeset after the word splash.
It will look like ro quiet splash nomodeset
Download Ventoy and install to USB. Drop the ZorinOs iso to that usb. If will boot from that drive you will see menu. Highlight Zorin and hit ENTER. Choose safe graphic to see if that is the problem. "nomodeset" is for graphic. I did that when installing Linux on Mac
Considering that you asked the ZorinGroup directly (Pro Support) and the long list here:
I think it makes sense we would not simply solve this on the first try.
The above covers most hardware in addition to software or BIOS settings.
The only thing that stands out to me is:
Both of these rely on the Integrated Graphics alone. I have a Nvidia 3060... And it is working perfectly. I suspect a 3070 should, too.
But the i7 graphics? It may not be, resulting in a complete inability to proceed.