I downloaded the 7 GB(!) microSD card from their website, and flashed it to a 128 GB microSD card using Balena Etcher.
Then I popped the microSD card into my dev kit board, plugged in HDMI and a USB-C 3A power supply, and waited... I kept seeing a giant NVIDIA logo on my display, and after about 20 seconds, it would seemingly reboot to black screen, then the logo... and repeat forever.
Searching around the Nvidia forums, I eventually found this issue: Nano 2GB boot looping, and finally found the problem: apparently the default image download is only for the 4GB Nano model.
I had used Google/DDG to find the getting started guide, and it linked to the 4GB kit guide—there's an entirely different URL for the 2GB kit!
So I went through that guide, downloaded its image, and flashed it to the microSD card. Now the Nano is booting like a champ.
Why do they have specific images for each RAM size? No clue.