Here are some ways to earn cryptocurrency without investing any initial capital:

1. _Crypto faucets_: Visit websites that give away small amounts of cryptocurrency for free, such as Bitcoin or Ethereum.

2. _Airdrops_: Participate in token giveaways or airdrops, where projects distribute free tokens to promote their cryptocurrency.

3. _Bounties_: Complete tasks or activities, like testing software or translating content, to earn cryptocurrency rewards.

4. _Crypto games_: Play games that reward players with cryptocurrency, like Axie Infinity or The Sandbox.

5. _Mining simulations_: Participate in simulated mining experiences, like CryptoMiningGame or MinerGate.

6. _Crypto rewards programs_: Join programs like Coinbase Earn or Binance Learn & Earn to receive cryptocurrency rewards for learning about different coins.

7. _Referral programs_: Refer friends to cryptocurrency exchanges or wallets and earn rewards in cryptocurrency.

8. _Crypto contests_: Enter contests, like trading competitions or prediction challenges, to win cryptocurrency prizes.

9. _Crypto-based freelance work_: Offer services like content creation or social media management and receive payment in cryptocurrency.

10. _Crypto giveaways_: Participate in community-driven giveaways or charity events that distribute cryptocurrency for free.

Remember, some of these options may require effort, patience, or skill, but they can provide a way to earn cryptocurrency without initial investment.