I hope you're right.
You have to define what you mean.
Government built by having policies that lead to it? Not only is it strong, it's the only possible way for it to happen.
Government built by saying 'let's print money and give it to the poor so they're middle class'? Of course not, that's a non-functional destruction of the economy.
You speak of it like it's a hypothetical, but we've *had* a middle class created largely from the government's policies already, as I mentioned.
The Estate Tax, the right of labor to organize, progressive tax rates (more than now), are all examples of such policies that are different from 'hand money to the poor'.
That's really a small part of things - the programs you seem to be thinking of might be things like Social Security and Medicare - or if liberals get our way, universal healthcare/medicare for all - which are not so much 'handing out cash' as providing essential services more efficiently/effectively than they had been when we had 90% elder poverty and many without healthcare, and what we still have, a bloated 'private' insurance industry extracting great wealth from society.
There's a reason why every other advanced nation, without the political corruption we seem to especially have on this, has a form of universal healthcare.
That has nothing to do with 'making a phony middle class that needs government handouts', and everything to do with society have an efficient economy for needs.
You say you agree a strong middle class is needed, but the policies you seemed to advocate are in contradiction. That's the problem - myths that you can do policies that are actually to help the rich at the expense of others the right is led to not understand hurt the middle class. That's the core of trickle down economics - "give your money to the rich. It won't cost you, you will get it back when they magically multiply it!" Nice story, but not accurate.
There was a test of 'who's right' on a national scale, when Clinton pushed his tax increase on the top 2%. Every right-wing commentator I can find with dozens on the record predicted disaster for the economy and their predictions were proven wrong. IIRC the deficit went down, not up; unemployment went down, not up; growth went up, not down, and so on. We rarely get such a spin-free test of who is right, and we got one, and the answer - even if the right ignores it.
Of course, long-term economic performance by who is in the White House is another suggestion. I did a review of 10 previous presidents, half of each party, and found that most rankings on economic indicators were again and again with the top 5 spots the Democrats and the bottom 5 the Republicans - looking at employment, growth, the stock market, etc.
The government isn't the economy - it is one major player. It's important for it to have the rules such that lead to productive results.
The bottom line is that the right's goal for the economy is one with huge wealth concentration and a far worse off middle class (owning less the rich can own instead, cheaper labor, etc.), and the progressive left is the one that wants a stronger middle class - partly at the expense of the rich, with such things as CEO's perhaps again 'only' making 50 times what their average employee does instead of 400 times, with higher taxation on great fortunes that increases prosperity and opportunity for others.