Can I establish a one person company(with no co-founders) in USA? Will this company be restricted or face barriers to grow regards to law?
Single owner limited liability companies and single owner corporations are permitted under U.S. law and provide full limited liability protection.
A single owner limited liability company is taxed either as a "disregarded entity" (a sole proprietorship if the owner is a natural person) or as a corporation, at the election of the owner.
A corporation with a single owner is taxed either as a "C corporation" or, as an S-corporation if it qualified to be one (the single owner must be a U.S. citizen natural person or one of a few special kinds of trusts).
A single owner business trust is also allowed (tax treatment can vary under different circumstances).
A sole proprietorship is the default choice and can operate under a trade name, but provides no limited liability protection, unlike other choices of entity.
If you reside in the U.S., but are not a citizen, your visa may or may not permit you to conduct various kinds of businesses through a company that you own. This depends on the nature of your visa, if any. A lawful permanent resident can conduct almost any kind of business although there may be some tax election choices that you can't make. Someone on a tourist visa, in contrast, is very greatly limited in what they could do with a company.
I think you're talking about a sole proprietorship.
In this era of rampant deregulation/non-regulation, I doubt that there would be many significant barriers to growth. If your company grows, you can always hire an attorney to help you figure out a way to deal with any barriers you do encounter.