Is a HC-SR04 fast enough to make decisions on moving robot (4 Johnson motors 300 rpm)?
On it's max speed, how far is it's braking distance?
Then you should start braking atleast from before that distance of the object.

Let's say your braking distance is 25cm, you should start braking >25cm.
But this is only when you would instantly brake at the moment you're within 25cm reach.

So we have to know how many distance we will travel during the calculation, before we start braking.
You could just try it out, set the distance a little higher everytime you crash into it (Assuming it doesn't fail and is always at the same time).

We have to know the top speed of your motor, RPM doesn't say a lot in this story, we'll need to know how big your wheels are to be able to determine how many cm's you'll travel per revolution, and doing that times the RPM, you know your top speed. (Or you can also measure this, but it can change depending on how full your battery is)

Also, your code should be real-time you'll likely want to use timers to trigger the trigPin and use an interrupt on the echoPin to be sure none of your code will delay your sensor. This will improve execution speed aswell as reliability/deterministic timing. Also, it will make it possible to run it aside from your regular code.

So if you know, your top speed = 10cm/second.

And you know that 1 calculation+reaction-time is 200ms.

You can safely assume that you need >2cm extra.

To be honest, you should add a little for when it's slippery/another surface or just so you won't touch the object.

So. The ping sensor is almost always fast enough, only if the calculated range is outside your max range, it will not work.
You could however, use an IR proximity sensor which will trigger at a set distance. This way you don't have to do any calculations and just brake whenever you receive the interrupt. But it won't tell you the distance to the object.

The cool thing on the distance sensor is that you can also scale the brake distance on your driving speed, so that it will brake later when you're driving on half your speed. That way you can come very close to an object, but still be 100% sure that you won't crash into it.