My understanding is that normal force is always equal to the applied force vector that is in line with it. Like weight going down, normal force going up along the same line, equal in magnitude.
Here is a case where I guess Newton's third law somehow doesn't apply:
I push a object with one of my hands. It starts to move and then accelerate. Therefore, I know the net force is bigger than zero.
According to user Wolphram Jonny in his answer to a similar question, the force received by the object as I push it is defined by the interaction.
Can someone perhaps answer this question by explaining how the "interaction" is involved here? the question I am talking about