A mature BI (one providing an above-poverty-line benefit) is an expensive proposition, but you don't need a mature BI, or one that replaces all the programs you'd like to replace with one, to get net social benefit from it. So you start with a small BI, and phase out the things it is eventually planned to phase out only as the BI benefit makes the existing program irrelevant. (Until then, you just treat the BI as income when calculating benefit for the existing programs.)
To do this, you establish a funding stream that is expected to grow with economic growth, and let the funding stream (basically; using a formula that cushions fluctuations so that short-term downturns don't lead to BI cuts), including prior year savings from reductions in other programs due to the BI along with tax collections in the "funding stream" calculations -- determine the BI level.