Not only is the exact release timing of the restock unknown, but it's not divulged whether or not the restock will include the $400 all-digital PS5, the cheaper model of the console that's been next to impossible to buy due to how limited its stock is.
What Randall does note is the restock will be limited to online orders only with in-store pickup, which means you're out of luck if your local Target runs out as there's no option for shipping.