The most recent flyover video of Tesla Giga Austin in Texas (January 17, 2022), shared by Jeff Roberts, reveals a small batch of about 9 Tesla Model Y, which very likely were produced at the site.
The first pre-production Tesla Model Y was seen at the plant in late August 2021. Several months later, in late December, it was rumored that series production of the Model Y might start within a week. A similar rumor was reported on January 10.
A sight of multiple newly produced cars in a parking lot, in front of the factory - connected to charging points (see from 8:47), would support the rumor that Tesla is starting series production or at least entering the final phase of preparations.