New TX resident-car registration questions

Brand new to TX y’all!

Following all the right steps to get our cars squared away – got insurance, inspections are done, yet, can’t find appointments available at our local tax office 🤷‍♀️to register – and you can’t look beyond Sept right now – when do they post availability for October? I want to pounce as soon as it’s open – anyone know when Oct appts can be made? Thanks!