What conditions cause a party to naturally occur?
According to this link, a party has a random chance of naturally occurring at dawn, and no conditions need to be met for a party to be naturally hosted- but I'd guess you'd need at least one NPC in your world to act as the host for a party.
Edit: I've tested the theory and have conformed that a party can naturally occur in a world without the need for a party machine. The world I used was a small, non-Expert mode pre-hardmode world. The only NCPs that had moved in were the guide, merchant, dye trader, arms dealer, demolitionist, nurse, painter, clothier, mechanic and dryad.