How to Access Forge in Halo 4 Without Xbox Live

Impossible. Forge requires Xbox Live Gold:

• Multiplayer feature relying on servers for map creation storage/sharing.
• Xbox Live mandatory for all multiplayer features (including Forge).

Even with the disc, a Gold subscription is required.

Offline Alternatives (Unofficial)

• Halo 4 Custom Edition: Unofficial, limited Forge offline (PC).
• Third-Party Tools (Halo Forge SDK): Create/test maps in simulation; technical, unsupported, security risks.

For full Forge, subscribe to Xbox Live Gold (or play on MCC PC where Forge is free with Xbox account).