The short answer
Can a foreigner start a business in Dubai?
Yes. Most Dubai mainland business activities allow full foreign ownership, while free zones have long supported foreign-owned companies. Particular strategic or regulated activities may still have additional ownership, licensing or approval requirements.
The more important question is not simply whether you can own the company. It is which company structure enables the business to operate in the way you intend.
A consultant serving international clients, an e-commerce business, a restaurant, an import-and-export company and a regulated professional practice may require very different licences, facilities, approvals and company structures.
Start with the activity, not the package.
Decide what you will sell, who you will invoice, where your customers are and whether you need staff, premises or UAE residency before choosing a jurisdiction.