Yes, if your business is a legal person that can sign a contract in its own name. No, if "sole proprietorship" means you personally, trading with no registered company. That distinction is the whole answer. It is also the thing the term hides. In one country a sole proprietorship is a registered entity with its own tax identity. In another it is just a person invoicing under their own name.
An employer of record arrangement has three parties: the worker, the client, and the provider. The provider becomes the worker's legal employer. It signs a commercial agreement with the client. So the real question is not about company size. It is whether there is a counterparty that can sign that agreement, be invoiced, and carry the duties in it.
When a sole trader can use an employer of record
Suppose you trade through a registered business. It has its own legal identity, a tax registration, and the power to contract. Then the arrangement works exactly as it does for a larger company. Nothing about an employer of record requires a minimum headcount. A one-person business hiring its first employee abroad is a normal case, not an edge case.
What changes at that size is proportion, not eligibility. The fee is charged per employee per month. On a single hire it is your whole overhead, rather than a line spread across a team. Model that before you commit. The maths that makes an employer of record obviously right at twenty employees is less obvious at one. The employer cost calculator shows the statutory contributions for the country you are hiring in. That is usually the larger number.
When it does not work, and what people do instead
Now suppose you are a sole trader in the everyday sense: an individual with no registered company. Usually there is no entity for the provider to contract with. You are not a business employing someone. You are a person who would be personally liable as an employer. Providers decline that shape. The reason is not caution. Employing someone creates statutory duties, and those duties sit on the employer. An individual carrying them personally is a very different risk from a company doing so.
There are two usual routes from there. You can incorporate first, which turns the question into the one answered above. Or you can engage the person as a contractor rather than an employee. The second route carries its own risk. Whether someone is genuinely a contractor depends on how the work is really done, not on what the agreement says. Getting it wrong is misclassification, and the liability lands on the engager. Our contractor classification tool walks through the tests one country at a time.
What to check before you assume either answer
Three things decide it. None of them is your size.
First, whether your business is a separate legal person from you. That depends on how it is registered, not on what you call it. Second, whether it can be invoiced and can sign a commercial agreement. Third, whether the country you are hiring into adds any requirement on a foreign client. A few do.