In a word: No.
Monopolies and other market distortions absolutely form without government. There are a number of reasons, but the chief one is geography.
Notice I said a "vast majority" of markets don't form monopolies, not all. There are a few that do, like some private road companies or telecommunications services where the number of providers is limited by the the 'physical capacity' of the area. That's fine. It's not necessary that every single market not be a monopoly in order to not have a large wealth gap develop and be beholden to the wishes of a few rich corporations.
The vast majority of markets for things like food, medical care, cars, shipping, trinkets, almost anything, would be competitive and free of monopoly. The only way that people truly gain an unfair advantage over other people is by using the institution that has the sole right to take people's money, restrict civil liberties, and decide the values/structure of the entire society. The fact that the supposed limit to such an enormous power, and what makes that power of government beholden to the will of the people, is something as flimsy and subject to corruption as representative democracy, was why the Founding Fathers favored not an unchecked democracy where the will of the easily led majority is king, but a government with limited powers kept in check by a severely limiting constitution. The notion of fair regulation is an impossible ideal because democracy is too easily exploited. Especially in our current situation where lobbyists abound and the wealthy corporations have such enormous financial influence on politics, it should be plainly obvious that regulations aren't going to be unbiased. Big agri-business executives and FDA regulators are pretty much the same group of people, FFS. There is also the fact that regulations are going to be necessarily bad since the free market competitive situation is already the optimum situation; any change to this situation is necessarily not optimum. The same thing applies for untold other industries. Regulation also costs a ton of money. They also violate rights and restrict freedom. The constant growth of government is why you are taxed at almost 50% - and for what?
Surely you agree that as it stands in the US, many of the regulations on the books are downright corrupt. Surely, with the number of regulations on the books and the goliath size of the bureaucracy, it's not the case that there is no regulation, as is often claimed. It must be, from your point of view, that there are regulations, but that they aren't of the right kind, right?