niezwłocznie

To be sure, he may not have seen it right off the bat.

"You see, right off the bat we have something important in common."

It's just not the kind of thing you say right off the bat.

People don't know what to say right off the bat when they see his work.

So he was saying, what if you hit that right off the bat?

I think he's going to play well off the bat.

That's really all I can think of right off the bat.

I got down to the real business at hand right off the bat.

The baseball off the bat was on top of him too quickly.

"Not a good sign when you have to say that right off the bat."