Yes, you can play Axie Infinity without spending any money. But to do so, you will need to join an Axie Scholarship Program. In these Scholarship Programs, people lend out their Axies to other players in place for an SLP reward split contract. In this case, the player can play the game for free without needing to invest to buy Axies. But the SLP reward that they earn is split between them and Axie's original owner. Usually, the player is expected to hit daily targets set by the original owner to proceed with their agreement.