When you say “start, stop, and restart again without resetting” I suspect you’re talking about not having to hit the top pusher, the bottom pusher, and then the top one again. If you want to be able to reset the chronograph at 0 in one press, it can be done if you have a flyback chronograph.
This is a particular complication for a chronograph, so if your watch could do this, you’d likely know already as part of your information from the purchase. Most chronographs require you to do as you said: stop the chrono, reset it with the other pusher, and start again.
If your chronograph is a traditional one like that, do not attempt to push the reset pusher when the chronograph is running. This can damage the movement. Although most offer resistance if you attempt to do so, I wouldn’t force it.
Hope that helps. What watch are you talking about?