Hey Kynan,
This is normally caused by drivers missing from WinPE. This can be confusing because of the different versions of WinPE, and what you are actually deploying operating system-wise. Lets say you are deploying Windows 10 x64 to a system. The driver you would be looking to add in WinPE may not be the same driver you would use for the target operating system. If you are in fact using WinPE 10 x64, then the NIC driver would be the same, but if you were using WinPE 5 x64, you would have to use the Windows 8 x64 version of the NIC driver for WinPE. I just mention this because sometimes the WinPE environment may not match the target operating system you are deploying. In your case however, I think you really are experiencing a DHCP issue as it is required for an out of the box configuration. If you present a DHCP server to your setup your issue would likely go away. Another alternative would be to issue static IPs to your clients in WinPE, but for that you would need to alter the out of box configuration of GSS because it is a core requirement for the default installation to have a DHCP server running. I'm pretty sure you can even introduce a dummy router that has a DHCP server running on it and connect it to your switch so it will issue addresses automatically. This may be an easier option than running a software DHCP server.
If this happens to solve your issue, kindly mark it as a solution. Thanks :)