Stadia AMA on Wednesday reported that on the first day you would have to use the Chromecast Ultra included with the Founder’s Edition. This evening’s Stadia Controller pairing seems to be available on existing streaming dongles already.
The bundled version of the Chromecast Ultra featured “the latest firmware” to play Stadia, according to Google this week. That said, in order to allow you to play on any connected TV, the company hopes to update existing devices “soon after launch.”
This seems to be already underway with several Chromecast Ultra owners (via Reddit) running version 1.42.172094 — the current stable — showing a link code for the Stadia Controller appearing on the screen. This takes the form of a pill-shaped bubble saying “Stadia Controller” followed by pressing various keys.
The code can be disabled from the Google Home app under Ambient Mode settings for those who do not use Stadia. Until Stadia launches on Tuesday, it is unclear whether game streaming is already working with current Ultras or whether it requires another firmware update.
The on-screen and in-app process for linking a Stadia controller has been fully detailed by Google this week:
If you already have your Stadia account set up on your Chromecast Ultra, use the Stadia Controller to choose the Stadia account you want to log in with. If you have not yet your Stadia account set up with your Chromecast Ultra, continue through the rest of these steps.
Use your controller to select “+” on the screen.
On your mobile device, tap your avatar in the top right corner of the Stadia app.
Tap Add account to Chromecast
[your stadia account]
Tap Done to finish setup, or tap Add a security pin to add a pin to your Stadia account.
[your stadia account] 
