The idiom "right off the bat" means immediately or without delay, right from the start or the beginning of something. Just like a baseball is hit off the bat right away, this phrase suggests taking action or reacting promptly.

I always thought it was a baseball term. Right off the bat means actions happen right away on contact. Runners are in motion, right off the bat. It can be applied as well to anything as soon as one action is completed, a chain of events occur too.

immediately

"Off the bat" means happening right away.

I can think of two right off the bat, cholera and cryptosporidium