If the definition of balanced forces is "two opposing forces that are equal" and an object with a net force of zero acting upon it means that the forces are balanced on the object, then it should follow that an object travelling through space at constant velocity should have a net force of zero acting upon it. But there was an initial force acting upon it when it was thrown into space. What is the force that is balancing that initial force to make the net force zero?
You are right. If we have an object at rest and then we want it to start moving, we apply a force to the object. While the force is being applied, the object accelerates according to $F=ma$.
Now let's say we stop applying this force. Then there is no longer a net force acting on the object. Therefore, the acceleration is $0$ and the object now moves at a constant velocity.
I'm not sure if I fully understand where you are having difficulty, but it seems to me that you are thinking of objects that can "remember" the "history of forces". So that if we apply a force and then take the force away, we still need to apply an opposite force to undo what the first force did to cause the acceleration to be $0$. This is not the case. Once the first force is gone, the acceleration is then $0$.
However, if we wanted to stop the object and bring it back to rest, then we would need to apply a force opposite to the first force to produce an acceleration in the opposite direction.
Side note, for this answer I am assuming we are in an inertial reference frame and just applying a force to an object. Any discussed motion or velocity is assumed to be viewed from this reference frame. I know I need to specify this or else I might get attacked by the relative motion police (of course, what constitutes an attack is also relative, so maybe let's just all agree to boost to a frame where we don't have to worry about all of this). :)