The official FAQ currently says the process should take weeks and describes expedited processing, but it does not guarantee a particular completion date. Test the deadline against the current published process for every candidate route.
Test the date against published process, not against price
Speed in immigration is produced by specific mechanisms: premium processing where a category offers it, port-of-entry adjudication where a classification permits it, or an expressly expedited process. Those mechanisms are documented, and where they exist they can be planned around without treating an estimate as a guarantee. A family should therefore write down the deadline, list the routes that could apply on its facts, and check what each route's official material currently says.
The Gold Card FAQ currently says its process should take weeks and describes it as expedited, but it does not guarantee a completion date. That may still leave the framework worth considering for other reasons, but it should not be chosen because an intermediary promises more than the official page does. Moving a school-year deadline is usually cheaper than paying for an outcome that remains subject to vetting and admissibility.