When phsicists talk about physics, they have given words to mathematical quantities. Ultimately, they are talking about measurable quantities that are well defined, and they are talking about equations. The 2nd law of thermodynamics is just an equation, and entropy is a well-defined physical quantity.
So, when you say that "The essence of time is change", we don't like it because you have not defined what essence or change are, in clear mathematical language. In other words, for us, it is philosophy at best, and nonsense at worst. It's the same when you say that the 2nd Law of Thermodynamics is a "driver of change". It doesn't mean anything. We also don't know what you're thinking of when you use words like "symmetry".
In short, no physicist can answer your question, since it is not a good question.
But it's okay. You seem to have a passion for physics. What science popularizers try to explain to the masses is indeed true, but it is hard to really grasp it without some formal background in mathematics and physics.
Physics is unfortunately hard, and even asking a question that is not nonsense is difficult, so don't panic. I encourage you to get some formal background in physics, or to keep reading and asking questions regarding what you have read, whichever suits you better.