The ability to work from a dynamic situation, someone stepping forward to grab, is done in ki society dojos, through ki timing. That is to say, you learn to move when the uke's intention or will is directed towards you. To do this, you need to develop a feeling of empathy or oneness with your uke.
Ki timing is different than physically reacting to uke's grab. If you just react to someone's attack, you're usually moving too late.
A common ki timing exercise is to have someone step forward to grab. When you feel their intention, or ki, come towards you, you say "One" out loud. The uke lets go and grabs again. Nage say "Two" when they feel Uke's intent. On the third grab, nage says "Three" and performs the technique.
It's important for the attacker (uke) to vary the timing of the attacks. You don't want to be caught up in a rhythm of attacks.
This sort of stuff is usually taught on day one or as close to start as possible. As was pointed out, it's a foundation that needs to be established, so other things can be built on it.