Yes it is possible, just like driving a car with your feet is possible.  That doesn't make it wise though.  
  
For example, simply post a thread here and offer to give anyone who posts a message an initial share of the coins.  There are many other ways to do it, all as equally useless.  What is not earned is not appreciated. 
 
If you mean, can you have a consensus algorithm based on how many coins each person has without anyone initially having coins.... well that's obviously a no.  This is why you need that proof-of-work period at the beginning.