First of all, there is no PCI (or PCIe) bus on Omega2, thus no go on that route.

Regarding USB-VGA output dongle:
It needs a driver on the MT7688 side (Omega2 side) and not only that,
it needs a large frame buffer on the Omega2. That USB-VGA dongle is just a data pump/VGA output formatter to continuously refresh/display the content of the frame buffer.
In such case, Omega2 does not have large enough memory, nor enough horse power to isochronously send the FB data out over USB.
In another word: dead-end.

Use the device as what its is most suitable for.
Your case needs a device such as Raspberry Pi zero.