This is not how gradient based NN optimization works. What you described is called "random weight perturbation", a variant of evolutionary algorithms. It does not scale to networks larger than a few thousand parameters for obvious reasons.

NNs are optimized by directly computing a gradient which tells us the direction to go to to reduce the loss on the current batch of training data. There's no trying up or down and seeing if it worked - we always know which direction to go.

SGD and RWP are two completely different approaches to learning optimal NN weights.