#2 and #3 are trivially obviously true.
Not so. Naturally occuring common property can be had without work, either of your own or by someone else. Nobody has to work to provide the air that I breathe.
And governments (or indeed, anyone else who produces money) can give that money away, without ever having taken any from anyone - indeed, they can't take any from anyone until they have first produced some and given it out, because nobody has any.
It's an interesting and unavoidable characteristic of fiat money that governments can't collect it as taxes, until after they've spent it.
As to history showing #1 to be true, that's a serious stretch. Very few attempts have ever been made; Failing at the first attempt (or even the first dozen attempts) to do something difficult is not a proof that that thing is impossible.
History showed it to be true that heavier than air flying machines were impossible. Right up until the Wright Brothers actually did it.
History simply isn't the kind of evidence that can show what you are claiming it to show.
Of course, it might be impossible. But it probably isn't, and as stated, the claim lacks a usable definition of "prosperity", and is therefore unfalsifiable (by any means, including a futile reference to history).
You cannot legislate the non-prosperous into prosperity by legislating the prosperous out of prosperity; But that's tautological.
What (if anything) wealth or poverty have to do with prosperity is a very complex question, which depends on how you define "prosperity", "wealth" and "poverty".
If prosperity is defined merely by wealth, then it's a simple arithmetic fact that you can legislate people into prosperity by legislating the wealthy to become less wealthy while remaining prosperous.
If the threshold of prosperity is $P, and there are ten people who have $0.5P, and one who has $100P, legislating that the wealthy person must give $0.5P to each non-prosperous individual results in a population in which all eleven residents have achieved the $P threshold, and are prosperous; Ten have $P, and one has $95P, so not only have you not reduced the wealthy person to a non-prosperous state, but he remains by far the wealthiest member of the subject population.
Of course, prosperity isn't usually defined merely in terms of exceeding a given wealth threshold. A wealthy person can easily fail to prosper, while a poor person can prosper without amassing great wealth. So the claim is essentially meaningless without a definition of what the fuck they're actually on about - it's not even wrong.
