It depends a lot on particulars of your product and what you think "starting my own business" means.
The laws are about creating legal entities not actual work.
Do you have a product? Is it a website of software application? Ship it and keep improving it based on feedback. Working on software in your spare time is not prohibited and even good products take time to become successful.
Do you want to charge for the product?
That becomes a bit more complicated because for accepting payments you might need some legal entity (i.e. a company). First try to setup payments (using PayPal or Stripe) simply in your name, without creating a company. If not possible, try setting up a company in your own country and use that.
The things that you cannot do is to register one of the legal entities that we call companies (llc etc.) in US and work for that company. This also blocks you from doing things that require such entity (like getting funding or hiring people).
Legal entity is not required to have a successful, income generating product or needed to work on such product.
In context of the law "work" is "work for recognized legal entity and being paid for it". You can't work as a cook for a restaurant but you can cook a dinner for your friend, even though both require the same kind of "work". Similarly, the law doesn't allow you to work for a startup in US and being paid for it but doesn't prohibit you from working on an open-source project or on your own project.