If you were standing on top of Mt. Elbrus (elevation: 5.6km above sea level), you could see the horizon roughly 271km away (assuming the horizon was at sea-level, there were no obstructions, atmospheric or otherwise, etc). The inverse of this is that if you were at sea level, 271km away from the peak of Mt. Elbrus, you could theoretically see the peak of the mountain.

So, assuming you weren't at sea-level, it's reasonable that you could see the peak of this mountain from 300km away.

However, seeing the peak of a mountain on the horizon isn't sufficient. You'd need to see a large portion of the mountain on the horizon in order to determine that it's actually the mountain you see in the distance, and not a closer peak that's less tall. This means that the observer would need to be at sufficient altitude themselves in order to view the mountain from this distance. I don't know enough about the math to calculate the necessary altitude required by the observer, but I would estimate an elevation of many hundreds of meters above sea level to be necessary. If anyone else can calculate this better, I would love to know how to find the answer myself.

Without knowing the general area of where you were, all I can say is that it sounds very unlikely.