It should be noted that the first time I went through the steps below, AirPort Utility told me it wouldn't work with a non-Apple base station. However, I repeated the steps, and somehow it magically worked [update: no it didn't]. I can [not] confirm that I am using an AirPort Express 802.11n (1st Gen) to extend the network from my Netgear Nighthawk R7000.
It should also be noted that the current firmware for my AirPort Express is 7.6.4 (older firmware) and the newest available version is 7.6.9. However, I am not updating the firmware just yet in case part of the update included Apple shenanigans to prevent the Express from extending non-Apple networks.
Update: Even after updating the firmware, I can't get the AirPort Express to pass the IP. The broadcast works and functions as if it is extending the range, but the IP (the internet) does not pass through to the device connecting to the AirPort. So instead, I am just running a long ethernet cable from the main router to the AirPort Express, creating a "new" network with the AirPort, and extending my signal that way.
The steps to set up your AirPort Express as an extender (this information is largely based on a Quora answer given by E.O. Stinson):
Make sure your wireless router is set to a static channel, and write down the router's MAC address.
Configure your AirPort Express using Airport Utility:
- Under Airport -> Wireless, set the Wireless Mode to "Participate in a WDS Network", and set the network name, security, password, and channel to match your router's settings
- Now you'll have a new tab: under WDS, set the WDS Mode to "WDS remote" and the "WDS Main" to the MAC address you wrote down for your router. Be sure to tick the box for "Allow wireless clients."
- Under the Internet tab, set Connection Sharing to "Off (Bridge Mode)."
- Click Update. Wait for the Airport Express to restart.