I was thinking more about the Scandinavian countries but France works too.
Also I was less looking for a single election/candidate and more how you could get there eventually and what forces could lead to that.
I get you, they're just bad starts.
Broadly I'd say the best case is to go back to the 1870s and start building a party then. David Davis was a reprehensible "Liberal" who wanted to support the Redeemers in the former confederacy but he was also a man very popular with labor. In the event that he were to get the Liberal Republican nomination in 1872, and then beat Grant there's a path where that party survives, merges with the Democrats and moves forward with the party veering further to the Left. I'd say you'd do better with the various movements of the post-Reconstruction Era Gilded Age that Ben Butler got himself involved in, but like the Populists who swallowed those IOTL movements, you do have to deal with the fact that the Agrarian element will probably be dominant for several decades.
After that I'd say the 1930s are a good choice though big reform is hard to avoid there coming from the mainstream. Hoover, eventually and pathetically came around to action to combat the depression though it was too little too late, Alf Landon in 1936 and Hiram Johnson also talked big games about Social Reform, but that would require the Republican left to roll several natural 20's to get the job done. The Democrats are in a similar position sans FDR. A Third Party movement could make progress then but must run a careful course between the likes of Huey Long, the Isolationists and the sort-of-socialists-sort-of-fascists that dominated the American populist forces of the era.
For a down and dirty pair of ideas that are closer to home, first I'd suggest having WWII go differently. If you can somehow cause the collapse of the Soviet Union in that war but still have the allies win it in a similar timeframe Henry A. Wallace might be able to maintain his position as FDR's VP or get replaced by William O. Douglas. Without the IOTL Red Scare and Cold War both men could probably do far more with their own Fair Deals then Truman aimed to or was able to manage.
And either related to that or separate, Walter Reuther was considered for JFK's VP in 1960. If he can keep out of Vietnam, well, there's a man to truly seize the Liberal Hour and drag it out into at least a Social Liberal if not Social Liberal with Industrial Democracy Couple of Hours. Instead of LBJ muttering racial slurs as he passes a Civil Rights Act there's someone who will actively try to change things because its right. And if we're lucky seek a Second Term in 1968.