The era of "progressive" (i.e. socialist) economic central control began in 1913, not 1940.
No, you're confusing means with ends. It's not
whether the government exerts influence on the economy, it's
why. It always does and always will, but towards what end is what makes the difference.
Prior to the late 1930s, all government policy was aimed at encouraging wide income gaps and maximum accumulation of private fortunes and capital. Labor movements were suppressed, often brutally. Income tax rates were kept as low as possible; the only time they were raised significantly was during and shortly after World War I, to pay for the war.
From the late '30s until the Reagan years, the government's influence went instead to narrow income gaps. Labor movements were encouraged. Income tax rates in the top brackets ranged from 70-91%.
Since the Reagan years, we've gone back to encouraging concentration of wealth and discouraging labor.
The middle of those regimens is as close as we've ever come to "socialism" in this country. We don't have socialism now, we have crony capitalism. There's a big difference, even though both involve government influence over the economy. If that's all you care about and you're blind to everything else, it may look the same, but it's not.