That's an insightful question, and shows that you aren't willing to accept things on their face value. With that kind of thinking, you'll go far in life.

FDR was well-known for latching onto little-known government programs, revamping them, and then re-announcing them as great examples of his "New Deal" policy. This is one more case of that. The early Social Security numbers were so short because almost no one ever collected on them (due to the difficulty in becoming qualified and in living to the retirement age), and thus, the program was all-but-unknown to the population at large. So, when he announced it, everyone assumed it was new, but all he did was to widen its scope to nearly all citizens.

I don't mean to pick on FDR; there are many other examples of this in Presidential politics. For example, the plans for the moon landings were planned for early 1970 ever since the middle of Eisenhower's term, but Kennedy decided to advance it by a bit (so that it would hopefully fall within his term of office) and announce it like some grand vision that he has. Reagan also learned about the secret project that Lawrence Livermore Labs and others were working on, and again, just redressed it a bit, his main contribution being the catchy name "Star Wars" -- it's assumed that if Reagan hadn't gotten involved and publicized it that it would have been fully deployed by 1985, but by getting Congress involved, it eventually got bogged down in politics and then killed.