If you start by replacing menial labor, there will be more unemployment but you’re not going to build the political will to do anything because those jobs were seen as “less than” and the political class will talk about how good and efficient it is that these jobs are gone.
You need to start by automating away “good jobs” that directly affect middle/upper class people. Jobs where people have extensive training and/or a “calling” to the field. Once lawyers, software engineers, doctors, executives, etc get smacked with widespread unemployment, the political class will take UBI much more seriously.
With white-collar jobs the threat of AI feels more abstract and localized, and you still get talk about "creating new jobs", but when robots start coming off the assembly line people will demand UBI so fast it will make your head spin. Either that or they'll try to set fire to them or block them with unions, etc. Hard to say when because another effort like the CHIPS act could expedite things.