Based on cases cited in one of your links, it appears that you refer to jurisdictions in the U.S.
Is there a mechanism for asking a Judge to review facts and
circumstances without going to trial? If so what is it called?
Yes. A case may be decided through motions for summary judgment or summary disposition.
In such motions, the moving party advances the proposition that the evidence is so one-sided that there is no reasonable possibility that the non-moving party could prevail on the matters at issue. Thus, the judge has a duty to ponder whether that proposition is permissible, which involves a review of the facts. If the judge concludes that the facts are reasonably indisputable, the judge grants the motion and the case is closed (meaning that it did not go to trial).
That being said, it is noteworthy that those are not the only grounds for filing a motion for summary judgment/disposition. A party may file such motion on other grounds that do not require a review of the facts. Scenarios that do not require a review of the facts are those where the statute of limitations has expired, the offense/tort/defendant is protected by absolute privilege, or the court lacks jurisdiction over the person or matter.
The Michigan procedural law that lists the grounds for filing a motion for summary disposition is MCR 2.116(C). The grounds involving a review of facts is formulated in 2.116(C)(10). Other jurisdictions have very similar provisions in their corresponding rules of procedure.