Earning $1000 without investing is reachable but it takes time. You can start little by little by joining airdrops and faucets. Those are all the free money, you just need time and patience to earn those coins. And for huge earnings, you can join bounties whichever suitable or comfortable for you. The signature campaign is one way of earning more profit backed with facebook and twitter campaign for additional profit. If the ICO succeed, then you can even earn more than $1000 though it takes 2-3 months before it pays off.
Yes it takes lot and lot of time to earn that money without investing anything, if you join a good bounty, you are lucky because most of the bounties today are scams, after you work for how many weeks you will not just paid.