Since you probably can't implement a sufficient UBI to provide an income floor that removes the need for other programs initially (at least, anytime soon), but instead need to start low and ramp up with productivity gains, you need a phase-in mechanism.

You can do this in a way that avoids forcing politicians to have the will to eliminate existing means tested programs but achieve that in effect by simply, add party of the phase in, specifying that UBI income counts as income in applying benefit formulas for existing programs.

It'll be much easier to kill each of the programs when no one has a low enough income to qualify for it.