How can the solicitor general enter a supreme court case even when the federal government is not a direct litigant?

The answer is " by writing an amicus curiae brief".

Companion of the court, or amicus curiae, briefs are regularly documented in re-appraising cases heard by the U. S. Supreme Court and state supreme courts, and also intermediate courts of bid. What's more, there is significant confirmation that amicus briefs have impact: Appellate courts regularly refer to them in issuing their choices.