Just run the app and configure the network to be wireless. At what point does this not work for your configuration?

The Play:1 isn’t supported in the in-app wireless flow, as far as I understand from the docs:

https://support.sonos.com/en-us/article/connect-sonos-to-a-new-router-or-wi-fi-network

And if you’re talking about during initial set up, I was unable to initially configure the Play:1 to connect to wifi before the firmware update.

While the unit is wired to the network, go to System Settings → Manage → Network → Manage Networks and make sure that your WiFi is listed.

If you have it on your network and can play music, just make sure wifi is enabled - maybe wifi was disabled by your parents. 

My WiFi is not listed there because I only have one Sonos unit and it is not configured to talk to WiFi, which is what I’m trying to fix without having to do a factory reset.

I ended up doing a factory reset anyway, to try one more time to bootstrap it wirelessly. Based on other comments I’ve seen online, I held the play button down for multiple minutes waiting for the light to turn from blinking orange to green. This has never happened, and it didn’t happen this time. This time I I got a new error during initial config: “Your product was added but may not appear in your system.” No amount of rebooting things fixed that. I finally found this reddit thread on the issue: https://www.reddit.com/r/sonos/comments/1dk67m0/product_added_but_may_not_appear/

Using the MacOS desktop app, I was able to -- I think -- roll out the needed firmware update without having to use an ethernet cable. I say I think because after the ethernet firmware update, neither my iOS app nor my desktop app can find the device. Without debug logs and a packet sniffer there’s not much more I can do on this issue. My sense is that I’m hitting some combination of user error and hardware obsolesence, and every time I try to start from scratch to do the “right” thing, I get it into a different inscrutable bad state. As an end user, one bad state looks pretty much like another. None of them give me clues as to what I might be doing wrong.

I’m about ready to give up on this, but I’m leaving these notes here for other people who stumble across this thread. And I’m grateful for everyone who has chimed in with advice. Thank you all for your time.

I’m puzzled. You can update and reconfigure your speaker whilst connected via an Ethernet cable. Once it’s done, ensure the wifi is enabled on the speaker. Then put in your wifi details. If you can’t do that, contact Sonos support and ask them to check the wifi card in the speaker - it may have failed. 

I don’t know what to tell you. Wifi is enabled (see attached images) but I have no option to enter wifi credentials.

Same issue here. Quite annoying. Did you manage to solve this? I haven’t tried yet, but perhaps it might work via the old Sonos S1 mobile app?

You can’t update the network settings, while the ethernet cable is connected, with a Play 1 unit. That’s the whole point of the original query. 

Once you have updated it in a wired setup - if you factory reset both the speaker and the Sonos App, it should then let you setup the speaker on the WiFi network - the WiFi network though needs to be 802.11b/g/n compatible with security mode WPA-2 personal and the Sonos mobile controller device needs to meet these system requirements…

https://support.sonos.com/en-us/article/sonos-app-requirements

Important Note: As the Play:1 is your one and only Sonos product, the previous system setiings/services will all be lost - so you’ll have to start from scratch.

Other helpful links:

Factory reset of Sonos product:

https://support.sonos.com/en-us/article/reset-your-sonos-product

Reset of Sonos App:

https://support.sonos.com/en-us/article/reset-the-sonos-app