I think you’d have trouble finding any civilization in history of notable population and duration that did not have some equivalent of a “middle class” - neither wealthy nobility nor destitute working class/slave/laborer. They might be craftsmen in one place, successful farmers in another, guild members in a third.
One of my high school history teachers remarked that you could say of any period in history that “a rising middle class began to assert itself politically.” Perhaps she wouldn’t say the same today… 
Every change in history not caused by geographic change was caused by a rising group or class sure they could run things better than the privileged assholes already there. 
And who promised to make things better for the serfs.
The board’s historians will be along to provide better answers, but I’ll offer some layman’s musings. 
Situations vary, obviously. Hunter-gatherer clans before farming was invented were probably mostly “middle class” with a few leaders at the top and a few slaves at the bottom. (This suggests that OP’s “natural state of human societies” is a poor term.)
Town dwellers have always been more prosperous than stoop farmers. Agricultural labor has always been the lower class. A household slave might be more prosperous and more “middle class” than an agricultural serf, even a tenant farmer technically not indentured.
In societies like medieval Japan, wasn’t the entire 90% below the Samurai caste a “lower class”? In ancient Rome and and ancient Greece, the slave class was smaller, but still large enough that non-slave citizens lived in luxury. If the slaves came from another race, and therefore weren’t “Roman”, you could say all Romans were middle-class or higher.
Cities had a large middle class. For example, 14th-century Genoa dock workers had a government-sanctioned union that paid for their medical care, etc. In fact, didn’t the Industrial Revolution* set back* labor? (For reasons similar to the concerns about automation today.)
The Black Death circa 1350 led to increased wages for the lower class due to simple supply and demand: the fever had drastically reduced the supply of cheap labor. Population levels recovered, but precedents had already been set.
I agree wholeheartedly.
Another thing that deceives us into redefining middle class is that the productivity gains of automation and industrialization meant that even the lower classes could enjoy luxuries the nobility could not even dream of a few centuries ago.
I’ve already mentioned cheap clothing. Cheap shoes, too. These once were things only the rich could afford beyond basic minimum. As for other things - Versailles had a theatre; aristocrats would have a musician group put on a concert or actors put on a play in their salon - or there was the lower class theatre in the public square. Today you can listen to music or watch movies at home even if you have a minimum wage job. There is plenty of humor about how badly people stank centuries ago because they seldom bathed, let alone sickness - how do you put a value on running water, modern medicine, and basic public hygiene? This is over and above an unhealthy amount of cheap food…
Perhaps a better definition then would be to define a “basic level” where people are in fact enjoying a decent amount of what modern North American society has to offer… Let’s say you are middle class if you can afford a car, your own place, a vacation once a year, some entertainment once a week or so… and perhaps to afford to raise two children. Then suggest what that would translate to in the great equalizer, money.
But one of the bigger problems with modern society, is that women are working. (Wait, that didn’t come out right… 
) The idealized 1955 lifestyle - for white males and their dependants - was that the man could work and the woman stayed home to raise the 4 children. As women joined the workforce, concurrently the cost of being the Joneses or keeping up with them also went up. Where a nice 1955 household would have a TV, record player and a radio, today we have electronic gadgets coming out the wazoo; we used to have a simple phone bill (my first phone line cost $7.95 a month) - now we have phone, internet, cable, cellphone, and perhaps subscriptions like Netflix. If both spouses are working, you need 2 cars. Even if only one is working, you need 2 cars. When I started working in the 1970’s, car-pooling was not a eco-friendly idea, it was a way for the other spouse to have the car during the day.
The worst offender is house prices. The limit on affordable house prices was the rule of thumb 33% to 50% of total after-tax income. With two spouses working the bar has been raised to the point that it requires 33%-50% of two incomes. (and raised further because of ludicrously low interest rates)
Also, as others have pointed out, the 1950’s were a magical aberration. The rest of the world was trying to rebuild from a war plus a shortage of working age males, while America had spent it’s capital over the previous decade building factories that could just as easily produce consumer goods in record numbers instead of war material, plus export to the rest of the world. Today, we have competition.
There’s been a modest benefit from the computer revolution, but the question is - where do the unemployed go? the change perhaps has been too fast. We’ve gone from agricultural to industrial to a service industry. As Amazon and Walmart decimate the retail trade, for example, what’s next?
So do you want to define middle class by occupation type? That’s not going to be easy.
As for nobility vs. upper class, there always was and always will be an upper class. Again, where do you draw the line? Own more than one house? Have servants? (Does the weekly gardener count?) Don’t have to work? that leaves out multi-millionaire CEO’s - their income level would drop drastically if they quit and went fishing.
Coincidentally, the New York Times has an article on this subject today.
Jared Bernstein on Clinton:
In other words, they talk about the middle class because that’s where they can make the most impact in terms of their electoral chances, not because there are more of them. But they presumably like hearing about their class growing and doing better.
Which only confirms my assertion that it’s a humpty-dumpty term that means whatever the speaker and each listener want it to mean, without all that troublesomeness of actually, you know, pinning it down to a specific group.
And in this case, it’s a matter of lifting us up until we are all above average.