All our current "overweening federal government" began about 100 years ago, with the Progressive era passage of 16th and 17th Amendments.
I agree, in part, with what you stated, above: The "progressive" era really began--well, if not 100 years ago, then about 80 years ago, with the Depressian-era reforms instituted by FDR. (True, Teddy Roosevelt--about 100 years ago--did style himself a "progressive"; but it was his fifth cousin, Franklin, who really set us on a path toward Big Government.)
Normally I'd stop with your words "I agree", and let it go with that, especially since the thrust of your comment is correct -- our current "Progressive Era" really got off the ground in FDR's New Deal.
But that would not have been possible without groundwork laid during the Wilson administration, 1912 to 1920, a hundred years ago -- the three major tools being the 16th & 17th Amendments, plus the Federal Reserve.
Yes, Teddy Roosevelt's administration (1901 - 1909) also gets a "fair share" of criticism.
However, when it comes to "Progressivism" as we understand it today, TR was the opposite of "talk softly, but carry a big stick".
Bottom line: except when paying for wars, the US Federal Government consumed roughly 2.5% of GDP from the administration of George Washington until the beginning of Woodrow Wilson's.
Then, as a gusher of revenues from the 16th Amendment arrived, the government began to grow, and has never looked back since.
Last time I checked it is around 24% and still growing.