In most cases the sweatshop employees do not have the freedom to leave their employer. They also do not have the economic freedoms to start their own companies.
Such sweatshop owners are guilty of slavery which is illegal under modern law (not biblical or religious law. Bible has no problem with such sweatshop owners).
The government that do not provide those employees with entrepreuneral freedoms is also immoral.
If a sweatshop owner provides it’s employees with freedom to leave the job and produce on his own in an economically free country, those sweatshops wouldn’t last very long.
A more interesting question would be whether the newly formed companies can compete with low production costs of a sweatshop before the sweatshop dies away due to lack of human resources?
The answer is yes. This is where technology comes in. As humans we have always sought to be more productive at a lesser cost by using better tools.
In an objectivist society some wise guy will make a living by selling manufacturing machines that can beat the sweatshop with lower inputs and higher outputs. And many gruntled employees will free themselves out of the sweatshop to start their own no-sweat shops that will beat the sweatshop. And sweatshops will not exist.
This is why there are no sweatshops in countries with economic freedom and individual rights.
Economic freedom and individual rights are the prerequisites for an objectivist society.