As a dentist, is it permissible for me to take out a usurious loan to purchase the minimum necessary equipment to open my clinic, given that I do not have sufficient funds for this and there are no Islamic banks in my country?

Borrowing with usury (riba) is strictly forbidden and is only permissible in cases of dire necessity, under certain conditions. These conditions include: the necessity must be present, not anticipated; there must be no other lawful means to alleviate it; and only the extent of the necessity should be considered. Based on this, your need to purchase tools for your project is not considered a necessity that permits borrowing with usury. You can look for lawful alternatives, such as buying the tools in installments or seeking another project. And know that Allah has promised those who are righteous ease and good provision.