In fact, you need a USB port on PC-1, which will act as a USB device for PC-2.
This is not possible for the vast majority of PC systems, because USB is an asymmetric bus with host / device architecture (or master / slave, if you want). USB controllers (and their ports) on most PCs can only work in host mode and cannot simulate a device.
That is why you cannot connect computers via USB without a special cable with specialized electronics.
The only exception is if you have a PC that supports the USB On-The-Go standard, which allows the USB port to operate both in host mode and in the device. USB-OTG devices do exist, but usually they are built-in devices (smartphones, etc.). I do not know if there is a way to add a USB-OTG port to a commodity PC.
EDIT:
If you donβt need a keyboard before loading the OS onto the PC-2, you can use a pair of Bluetooth USB dongles - one on each PC. You will need to use specialized software on PC-1, but it is definitely possible - I have already seen a possible implementation in Linux , and I am sure that there should be one for Windows. You will also need the Bluetooth HID drivers on PC-2 if they are not already installed.
On the other hand, have you considered a pure software / network solution such as TightVNC ?
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