You don't seem to understand how time works. Time is our perception of the passing of events. If time stops for a baseball, that's what it perceives. It's still there. It doesn't cease to exist or continue to exist in one particular time.

If I put you in a freezer and dropped the temperature to 0K, time would literally freeze for you. The passing of time would stop for you. It wouldn't for everyone else, though.

When the baseball hit the speed of light, it would experience that same situation. However, due to the acceleration that the thrower put on it, it would continue to increase in speed. When its velocity reached a speed greater than that of light, it would, effectively, teleport to its implied destination. It wouldn't do it instantaneously, but it would go faster than mass is capable of.

kthxbye

What is it they say about silence being golden?