Anywhere in unincorporated Grayson County the build starts with the OSSF division, and they will not accept an application at all without a current 911 address and the property ID number off your tax statement. Nothing gets built until they issue an Authorization to Construct.
Before that, a licensed site evaluator or a licensed professional engineer has to evaluate the site and decide what the ground will take. If the soil will not support a conventional system, which on this clay is common, a registered engineer or a registered sanitarian has to design a non-standard one instead.
The county quotes five to seven days for the permitting itself once the paperwork is complete. What actually sets your timeline is the site evaluation, and the engineered design if you need one.
An aerobic system also carries a two-year maintenance contract that gets renewed thirty days before it lapses, for the life of the system, plus an Affidavit to the Public filed with the county clerk recording what the property is on.