Quezon didn't "convince" the US to release the Philippines.
Instead, the US had always intended to grant the Philippines independence, once they were deemed fit for self-rule. The Americans viewed themselves as taking on the noble role of giving the Filipinos the education and experience necessary for independence. (Personally, I wouldn't compare the American colonization of the Philippines to the British and French Empires.)
Of course, many a rapacious conqueror in history has claimed similarly-benign intentions. But the subsequent and fairly-brief history of the Americans in the Philippines suggests that they were largely sincere and followed through with their promises:
The report of the First Philippine Commission (1899) argued that the Filipinos were unfit for self-rule and required American tutelage. (I couldn't find the full text of the original report, but this 1899 newspaper article contains some excerpts.)
The preamble of the Philippine Autonomy Act (1902) reads:
WHEREAS it was never the intention of the people of the United States
in the incipiency of the war with Spain to make it a war of conquest
or for territorial aggrandisement; and
WHEREAS it is, as it has always been, the purpose of the people of the
United States to withdraw their sovereignty over the Philippine
Islands and to recognise their independence as soon as a stable
government can be established therein; and
WHEREAS for the speedy accomplishment of such purpose it is desirable
to place in the hands of the people of the Philippines as large a
control of their domestic affairs as can be given them without, in the
meantime, impairing the exercise of the rights of sovereignty by the
people of the United States, in order that, by the use and exercise of
popular franchise and governmental powers, they may be the better
prepared to fully assume the responsibilities and enjoy all the
privileges of complete independence
This was followed by the Jones Law (1916) and the Philippine Independence Act (1934) (a.k.a. Tydings-McDuffie Act).
Of course, one could argue that Quezon was a capable leader. But just like later leaders of independence movements in the British and French colonies, the timetable for Filipino independence would probably not have been very different, even if Quezon had never existed.