If socialism is going to work, it must be built atop a free market.
Entirely wrong, that is exactly the opposite of reality, the exact opposite of what works.
Socialism works quite a lot better if it tolerates well-regulated markets in luxuries, non-essential goods and services....as long as they don't make life worse for everyone and aren't corrosive to society, human well-being, or the environment.
You can't patch up laissez-faire capitalism by layering a few welfare programs on top, we've got decades of evidence proving that. They're inherently just band-aids, not solutions, because the solution is antithetical to capitalism.
By contrast, we've got decades worth of experience in northern europe and (in, more limited form, many other places around the world) showing that democratic socialism with well-regulated markets alongside DOES work extremely well...at least, it does until the international finance industry (aka Wall Street, american business) gets big and powerful enough to fuck it up.
Also, there's no such thing as a free market. It's a fictional ideal, a thought experiment, not a reality (and never has been)...and, without regulations preventing it, markets always tend towards monopoly capture.
a rising tide lifts all boats;
You're quoting trickle-down bullshit? and you somehow expect to be taken seriously?