Can I pump my blocker after the attacker has chosen their order, before damage assignment?
In response to the comment, it is true that combat damage no longer goes on the stack.  However, the fact that combat damage no longer goes on the stack does not affect the answer to your question.  Assigning the order of blockers is part of the Declare Blockers step:


  509.2. Second, for each attacking creature that's become blocked, the active player announces that creature's damage assignment order, which
  consists of the creatures blocking it in an order of that player's
  choice. (During the combat damage step, an attacking creature can't
  assign combat damage to a creature that's blocking it unless each
  creature ahead of that blocking creature in its order is assigned
  lethal damage.) This turn-based action doesn't use the stack.


After that, you get priority, still during the Declare Blockers step:


  509.5. Fifth, the active player gets priority. Players may cast spells and activate abilities.


So you can use Giant Growth to save all your soldier tokens.

(Unless the attacking creature has Deathtouch.  In that case, one damage is considered lethal, so a 4/4 can kill four blocking 4/4 creatures.)