How can I attach my wireless printer with a WPS button to my router (Google Home Nest) which does not have a WPS button?

Solution 1:

This should be mentioned in the Installation manual that came with the printer.

Connect the printer using USB to a Windows or Mac computer.

You can now configure the Wifi settings manually using the Samsung Easy Wireless Setup program that came with the printer on the driver-CD or that you can download from the Samsung website.
The software saves the settings to the printer. After this you can disconnect the USB cable and use the printer via Wifi without having to use WPS.

Solution 2:

Even though it does not appear to be the OP's problem, I'd like to suggest others (possibly arriving here like me after struggling for ages to connect their HP printer to a Google Nest Wi-Fi Router) try and disable WPA3 in the Google Home App Wi-Fi settings.

Apparently, Nest Wifi tries to accommodate WPA2 devices even when set to WPA3 mode, but some devices, most commonly HP printers judging by other forums, aren't able to handle a WPA3 network even in backwards compatibility mode.

Took quite a bit of trial and error to stumble upon this solution, but once you know exactly what you need to google, you do find others who encountered exactly the same issue and solved it the same way.