When was the view formulated
Depending on the context, the name of this view is called "progressivism". Fundamentally, this view has its roots in the Renaissance philosophy of reason and its later Enlightenment cousin.
Kant, for instance, has a strong insistence that what we need to do is realize our rationality and through this establish a cosmopolitan society guided by reason (which he calls a "church" in Religion within the bounds of Reason Alone but which may be misleading if thought of as a place where people worship a divine God that makes pronouncements from Mt. Sinai).
Hegel offers a version that has the evolutionary element you're seeking. In that Hegel, all things are necessary in the progress of Geist, sometimes translated "spirit" and less frequently "mind." And this this simultaneously represents the unfolding of necessary logic.
There were also version based on advents in science. The timing of these views and their particular beliefs also supply one of the more interesting arguments against a belief in universal progress.
A mid 19th century view took the belief that then current physics had explained everything and we just needed to wrap up a few details. (And then came the https://en.wikipedia.org/wiki/Ultraviolet_catastrophe).
In the late 19th / early 20th century version, a version built around evolution was floated. It turned to a belief in phrenology (quite popularly believed at the time) and eugenics (which held that belief that some races are superior to others).
Early 21st Century versions benefit from better science so arguably they are the best presentations that invoke the views of the modern liberal state.
What are the counter arguments?
There's three avenues of counterargument that seem possible to me.
First, it's not obvious that progress is inevitable. It's difficult to come up with a naturalistic reason why it must be so. Why assume everything is moving forward? The Stoics assumed everything was a giant cycle that recurred, and the only thing we can change is our attitudes. Some religions assume things are heading towards a horrific apocalypse.
Second, naturalistic progress is not necessarily the progress we want to be inevitable. In other words, if a new superbug appears and kills the human race, is this "progress" in the relevant sense or do we mean something that relates more to goals we might appreciate.
Third, many of the previous examples had visions of progress that we would today see as morally flawed. Mussolini's Italy doesn't strike me as the sort of place I would want to live -- and not merely due to my own ethnicity. Moreover, these ideas were the scientific vogue of their time, so it's not so clear that the ideas that get wiped out and replaced by whatever people call science at a given time are the ideas that are wrong. (racial slavery, for instance, was an idea that grew on people in Europe in a way that it did not previously exist).