This is an interesting question, but it seems that people a lot smarter than me have debated it for centuries. You have strong support for your position, which is called the declarative theory of national sovereignty. Here's the opposite side of that debate first.
The constitutive theory of statehood defines a state as a person of international law if, and only if, it is recognized as sovereign by other states. This theory of recognition, was developed in the 19th century. Under it, a state was sovereign if another sovereign state recognized it as such. Because of this, new states could not immediately become part of the international community or be bound by international law, and recognized nations did not have to respect international law in their dealings with them. In 1815 at the Congress of Vienna the Final Act only recognised 39 sovereign states in the European diplomatic system, and as a result it was firmly established that in future new states would have to be recognised by other states, and that meant in practice recognition by one or more of the great powers.
One of the major criticisms of this law is the confusion caused when some states recognize a new entity, but other states do not. Hersch Lauterpacht, one of the theory's main proponents, suggested that it is a state's duty to grant recognition as a possible solution. However, a state may use any criteria when judging if they should give recognition and they have no obligation to use such criteria. Many states may only recognize another state if it is to their advantage.
In 1912, L. F. L. Oppenheim had the following to say on constitutive theory:
...International Law does not say that a State is not in existence as long as it is not recognised, but it takes no notice of it before its recognition. Through recognition only and exclusively a State becomes an International Person and a subject of International Law.
By contrast, the "declarative" theory defines a state as a person in international law if it meets the following criteria: 1) a defined territory; 2) a permanent population; 3) a government and 4) a capacity to enter into relations with other states. According to declarative theory, an entity's statehood is independent of its recognition by other states. The declarative model was most famously expressed in the 1933 Montevideo Convention.
Article 3 of the Convention declares that statehood is independent of recognition by other states. In contrast, recognition is considered a requirement for statehood by the constitutive theory of statehood.
A similar opinion about "the conditions on which an entity constitutes a state" is expressed by the European Economic Community Opinions of the Badinter Arbitration Committee. The Badinter Arbitration Committee found that a state was defined by having a territory, a population, and a political authority.