Installing Windows 7 x64 on a computer with only USB 3 ports

There is a tool for exactly this case supplied by intel. It slipstreams the drivers into the installation media in a way that it will also work once installed (I only tested it with an EliteDesk 800G2 SFF but I doubt it has changed that much). Be careful to chose the right version to download, there is a different one for Win7 and Win8 or higher.

Also the tool is a little finicky, you really have to have the image on a usb drive it can not be unpacked into a folder for some reason.

EDIT: As it seems intel removed their own tool because it did not work all the time. They now recommend to use a tool by gigabyte in cases where PS2 devices do not work. It can be found on this page and is named Windows USB Installation Tool. I have no experience with this tool but it is the official recommendation at the moment.

An alternative to injecting drivers is checking your UEFI/BIOS for a legacy USB mode.

This, as I understand it, presents the peripherals directly to the operating system (perhaps as if they were plugged in via ps/2). Once windows is fully installed, you should be able to go back into BIOS and disable that option.

This question has more information on this mode; What does "Legacy USB Mouse" support in a BIOS mean?

I successfully installed Windows 7 on a laptop with a USB 3.0 root hub by using NTLite.

It will allow you to insert the USB 3.0 driver inside your Windows 7 ISO.

NB: You don't need to buy a license for NTLite, the free version is enough for this use.