Government, doesn't create economic classes. They can assist people to do better. Which is where things like education, infrastructure, a modern working regulatory state, a tax code that encourages expansion and economic growth, a safety net for people who are struggling, etc. Government can also encourage people not to do well. We have ghettos, because of public housing being concentrated in low-income communities that have low education and high crime rates. Families with mothers who don't have the skills to take care of their kids and where their father of their kids are out of the picture, etc.
The New Deal was not an economic policy, or ideology. But the creation of the American safety net that is today even with the Great Society is still much smaller than European welfare states. I and others left and right would argue that is a good thing. But that our safety net need to be better, not bigger and designed to empower people to take control over their own lives. And not leave them in poverty. Which is really a different discussion. It wasn't the New Deal that created the American middle class. We already had one before the Great Depression. Just like the New Deal didn't get us out of the Great Depression. Since we were still dealing with the Depression at the start of World War II.
The role of government at least in a free society with a private economy is not to manage the economy. But to see that there is an environment where the most people possible can succeed. Which is what I mentioned in the first paragraph. Quality education for all, a national modern infrastructure system, a tax code that encourages economic growth, a modern regulatory state that does the same thing, while at the same time protects consumers and workers. You want government to promote your trade and your products and a safety net that empowers people to get up on their own feet. Doesn't hold them down with a few extra bucks. And then let the people make the most of the economy that they put into it and collect the results from it.