Like most grammar, I believe that it would depend on the way it is being used.
Are you throwing your self into the street, as in into on-coming traffic? Throwing yourself onto the street implies that you are dropping your body on the ground.
Are you taking your first step onto the street? It fits perfectly into this singular phrase.
Defining a location and making it plural changes it again! I am taking my first step into the streets of Harlem.
That is the fun/frustrating part about language.