The OP is way too vague and general to have much meaningful response.
FDR is the best candidate, but even he requires a bunch of ifs and nuances. What was important about his presidency was the way the country’s mood changed almost overnight. The appearance of doing something about the Depression was hugely important even if the economic indicators changed very slowly. You can argue that it took four years, or his whole first term, for a real recovery to occur, but because of that recovery he started in 1937 removing the stimulus programs that caused it and the economy immediately tanked. IOW, you can hurt the country very quickly but improvement is usually slow. It’s also true that the range of social programs and the appointment of more liberal Supreme Court justices had a profound effect, which is what we now call the New Deal, more so than the programs of 1933. It’s hard to estimate how quickly that changed the national picture. WWII had so overwhelming an impact that it muddies the waters.
Social Security took decades to make a big impact on the country. A change in social security today would require additional decades for those changes to take effect. The Supreme Court decision in Brown v Board of Education was in 1954 but it took the 1964 Civil Rights Act to shift the country and that took decades to have a real effect, even though certain things changed immediately.
If pressed, I’d restate what I just said. A president can change the conversation very quickly. But it then takes time for those changes to ripple through the country. And the president usually lags society, or at least lags the change actors in society, rather than leads. No president has ever made a lasting change that wasn’t already in the air waiting to be made.