Only one creature is required to block Gaea’s Protector. Other creatures may also block it, and are free to block other creatures or not block at all.
The defending player, not you, chooses which creature blocks Gaea’s Protector.
If each creature the defending player controls can’t block for any reason (such as being tapped), then Gaea’s Protector isn’t blocked. If there’s a cost associated with blocking Gaea’s Protector, the defending player isn’t forced to pay that cost, so it doesn’t have to be blocked in that case either.