If TR and the Progressives managed to win in 1912, how would this effect womens rights? Would women get the vote earlier then IOTL? Would this happen before ww1, or possibly before the 1916 election?
A sympathetic President is not the same as a Constitutional amendment. It needs 36 state legislatures + two thirds of both Houses of Congress.
Surprisingly, TR wasn't super-human.
No he was not but he understood politics, the press, and could spin public opinion rather well. More over TR is pretty close to being super-human given his accomplishments in life. I do not know of many Americans who can claim to have been a governor, soldier, author, explorer, rancher, police commissioner, and more. Honestly his personality was such that if he wanted women to get the vote he would go for it with everything he had.