How would a 'non scientist' propose a hypothesis in such a way that it would be considered and tested by scientists?

Hypothetically, if a person, without formal and extensive education in a particular scientific field, thought up a way to solve an unsolved scientific mystery… how would that person present that hypothesis in the right way and in front of the right people, to be taken seriously and have it tested. Although, it is unlikely that someone without proper formal education and scientific and mathematical background could solve such a problem, If someone thought they had ‘something big’, what should they do? What should be the next step. And sorry about the almost run on sentences.

PS I’m the person