Does a creature with zero toughness die immediately when it enters the battlefield?

Whenever a creature has toughness 0 or less, it dies the moment the game checks state-based actions. These checks happen continuously whenever a player would receive priority — meaning as soon as a creature with 0 toughness enters the battlefield, state-based actions are checked before any player can cast spells or activate abilities, and the creature is put into the graveyard. This is defined in CR 704.5f.

This is not 'destroying' the creature — it is a state-based action, so abilities that prevent destruction (like indestructible) do NOT save a creature with 0 toughness. Only effects that raise the toughness above 0 can keep it alive. This distinction is important and comes directly from CR 704.5f vs. CR 702.12 (indestructible).

Note that a creature may enter with 0 toughness because of its printed stats, or because a toughness-reducing effect applies to it on entry. Either way, the result is the same — it never 'survives' even a single moment on the battlefield from any player's perspective in terms of taking game actions.

Example: You cast a 1/1 creature into a battlefield where your opponent controls an active Engineered Plague naming your creature's type, giving all creatures of that type -1/-1. Your creature enters as a 0/0, state-based actions are checked immediately, and it is put into your graveyard before you or your opponent can do anything. Even indestructible would not save it, but a Coat of Arms-style +0/+1 boost applied on entry could.