Darksteel Forge gives all artifacts you control the indestructible ability (CR 702.12). Indestructible means a permanent cannot be destroyed by effects that say 'destroy,' and damage that would be lethal is not enough to destroy it either (CR 702.12b). Since artifact creatures are artifacts, they fall squarely under Darksteel Forge's protection.
Wrath of God says 'destroy all creatures' and also prevents regeneration. However, because indestructible permanents simply cannot be destroyed (CR 702.12b), the 'destroy' instruction fails to do anything to them. The regeneration-prevention clause is irrelevant since indestructible doesn't use regeneration at all.
It is important to note that indestructible does NOT protect against effects that say 'exile,' 'sacrifice,' or reduce toughness to 0 or less via -X/-X effects (CR 702.12b). So a card like Merciless Eviction choosing artifacts, or Toxic Deluge giving -X/-X, could still remove your artifact creatures even with Darksteel Forge in play.
Concrete example: You control Darksteel Forge and a Steel Overseer (an artifact creature). Your opponent casts Wrath of God. Wrath's 'destroy all creatures' effect applies, but Steel Overseer is indestructible because of Darksteel Forge. Steel Overseer remains on the battlefield; only your non-artifact creatures are destroyed.
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.