The same way we’ve seen other concessions become implemented. The same way universal healthcare, public retirement funds, universal education, student-wages, maternity leave, paid vacations, free public infrastructure, public housing and the like has become implemented before.

These came by as a result of strong labour movements and a general mass movement working towards getting specific goals implemented. These movements eventually forcing the capitalists hand.
I don’t think these mass movements formed around a core ideology generally - at least not as far as I can tell from the examples I can think of (for example the soviets’ call for “peace, bread and land” the cuban revolutionaries focus on working the local community, the maoists focus on helping the locals as well).
The movements were formed by an ideological core group. That core group gained support from the masses by way of working towards specific goals that alleviated suffering and improved conditions. Other stuff came after.
That’s a very condensed walkthru of my general understanding of historical labour movements and then a sidetrack into revolutionairy movements because I can’t avoid getting sidetracked. It’s very reductive and lacking in many areas, and there are many other ways of analysing these events, I know.

Maybe UBI can be such a cause that helps gain mass support. Maybe it can’t, I don’t know. Maybe it’s just a singular concession that cannot be a part of a greater movement, but then that concession still seems to be a thing that would make life better for people within the system. Maybe it’s a pipe dream, I don’t know, we’re talking hypotheticals.