Thanks to DJBenson, who posted the instructions below:

Log in to https://home.nest.com with your credentials then browse to https://home.nest.com/session in the same tab, you will see a JSON object of your session. Look for the string enclosed in the quotes after “access_token” and copy that to the clipboard (copy the full string between the two quotes).

It looks something like this:

{“2fa_state”:”none”,”access_token”:”REDACTED”…

In your Homebridge config.json, remove the email and password fields and create a new parameter called “access_token” like such:

{
"platform": "Nest",
"access_token": "***REDACTED***,
"options": [
"HomeAway.AsOccupancySensor",
"Protect.MotionSensor.Disable"
]
},