Suppose there is a wooden block resting on a friction less surface. You give it a little push (force, F) and then it starts moving. Since there is no friction acting on the block at its bottom surface, would you feel a counter force against F? If you feel it, does this originate due to the friction acting on particles/ molecules (because you are pushing those molecules) those make up the wooden block?
According to Newton's Third Law, each force has an equal and opposite reaction force. In this case, the reaction force will be the same as if you pushed the object on a surface which did have a non-zero coefficient of friction, but in this case, the object would gain velocity faster, because there was no friction force countering the force applied by your push.
The force you feel when you push on the object, or any object, the reaction force you feel is due to the object's inertia, its resistance to change in motion, as described by Newton's First Law.
The difference between an object on a surface with friction and an object on a surface without friction is simply the resultant acceleration of the object after the forces are applied, not the reaction force on your hand when you push it.
If you could travel through space freely, at any velocity you like, and you flew to the moon and tried to push it, you would still feel a reaction force against your hand, because you're pushing against the surface. Is there a wall behind the moon that is preventing you from pushing it through friction-less space? No, it is simply the mass of the moon that resists the change in velocity that you are trying to impose on it.
Forces do not exist to balance each other out.
Forces exist to cause acceleration.
So, yes, to accelerate something, you need a force. This is Newton's 2nd law: $\sum F=ma$.
Newton's 3rd law then says that this force, you apply on something else, is also applied on you backwards. This reaction force is still not friction, since that is still not present. It is merely the resistance of this object to start moving, which you feel pushing back.