I don’t know the history of SSI and Medicaid well enough to give you an exact time table.
In 1984, my Green Card girlfriend’s parents immigrated and her Father qualified for SSI and Medicaid because he was 65.
As to younger disabled immigrants, back then, I don’t know.
In 1971 when I immigrated you had to have a good employment record and be willing to work...
you were deported if you applied for any kind of government assistance...