According to series creator Don Mancini, Chucky most closely resembles his look from from Child's Play 2 (1990) due to it being the "fan favorite" design.
The opening shot is a direct homage to the opening of John Carpenter's Halloween (1978).
A woman in a red coat with a silk scarf covering her hair can be seen at the yard sale. This is intended to be Tiffany Valentine (Jennifer Tilly).
Although the year isn't referenced, the series was originally intended to take place in 2017. If still the case, that means the events here occur either right before or right after the events of Cult of Chucky (2017).
Don Mancini has stated in interviews that the rocky dynamic between Jake and his father, Luke, over the former's sexuality is based on the strained relationship he had with his own father growing up.