You probably want the initial value to be high enough that you can actually displace some existing means-tested aid programs, even though you may not initially be able to do all of them.
Slight adjustments in the number of beneficiaries doesn't really get you much benefit in terms of eliminating the inefficiencies of existing programs (in done ways out actually exaggerated them since there is a fixed component of the overhead costs for each program.) The real efficiencies Congress when you are able to eliminate programs altogether.
One benefit of that kind of ramp up is that it naturally phases out existing programs, making them easier to kill when their time comes (and much clearer when their time has come).
It also means (to the risk point above) that if we discover some ruinous dynamic caused by the UBI, we can more easily scrap it and fall back on existing systems.
Also remember that the average person breaks even, so affordability isn't really an issue.