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At what point does a creature/artifact/whatever become a legal candidate for being sacrificed to pay an activation cost?
For example, suppose I cast an artifact creature spell, and my opponent responds with an instant that would kill it (like a Lightning Bolt). I have an Atog that lets me sacrifice an artifact to give the Atog +2/+2. Can I use the artifact creature, even though the spell that "summoned" it has yet to resolve, to pay the Atog's ability's activation cost?
A card on the stack is not a permanent, so you may not sacrifice it.
When a card refers to a permanent type, like "artifact" or "creature," it refers only to permanents — meaning a card on the battlefield. Note that this includes the Lightning Bolt spell in your question — you can't sacrifice the creature until it is on the battlefield, but your opponent can't Bolt the creature until it is on the battlefield, either.
Cards in other zones are referred to as cards — e.g. Unburial Rites: "Return target creature card from your graveyard to the battlefield." — or spells if they're on the stack — e.g. Essence Scatter: "Counter target creature spell." (Compare to Murder, which affects creatures on the battlefield: "Destroy target creature.")
No, but it's not a valid target for Lightning Bolt either.
If it's not a permanent, it's not a valid object for a sacrifice payment.
701.14a To sacrifice a permanent, its controller moves it from the battlefield directly to its owner’s graveyard. A player can’t sacrifice something that isn’t a permanent, or something that’s a permanent he or she doesn’t control. [...]
If it's a spell, it's on the stack, it's a not on the battlefield, and it's not a permanent.
110.1. A permanent is a card or token on the battlefield. [...]
111.1. A spell is a card on the stack. [...]
111.1a A copy of a spell is also a spell [...].
For example, suppose I cast an artifact creature spell, and my opponent responds with an instant that would kill it (like a Lightning Bolt).
He can't do this. It's not a creature until the spell resolves to become a permanent. The same reason preventing you from sacrificing it to the Atog (not a permanent yet) is preventing him from targeting it with Lightning Bolt.
109.2. If a spell or ability uses a description of an object that includes a card type or subtype, but doesn’t include the word “card,” “spell,” “source,” or “scheme,” it means a permanent of that card type or subtype on the battlefield.
He has to wait for your artifact creature to resolve. (In fact, it's presumed he did if he casts Lightning Bolt targeting it.) In response to him casting Lightning Bolt, you may activate your Atog's ability using your new creature as the sacrifice.
Compare Lightning Bolt with Bone to Ash.
At what point does a creature/artifact/whatever become a legal candidate for being sacrificed to pay an activation cost?
When it enters the battlefield. This happens when the spell or ability that creates (usually, "summons") it resolves. (Though note that "summon" is no longer a word with any official meaning in the rules.)
It's worth noting that a creature becomes eligible to be targeted by Lightning Bolt, or anything else that says "target creature," at the same time it becomes eligible to be sacrificed.
Also at the same time, the object switches from being a "spell" (or "creature spell"/"artifact spell"/etc.) to being a "permanent" (or "creature"/"artifact"/etc.)
