Yes, girls can go Super Saiyan.
The Dragon Ball franchise features several female characters who achieve the Super Saiyan transformation, demonstrating that it is not exclusive to males. A prominent example is Caulifla from Dragon Ball Super. She is a Saiyan from Universe 6 who learns to transform into a Super Saiyan and even progresses to more advanced forms, such as Super Saiyan 2.
The ability to transform into a Super Saiyan is tied to the Saiyan race's inherent potential and their ability to harness ki (energy), rather than being limited by gender. Through rigorous training and experiencing intense emotions, female Saiyans can unlock and master the Super Saiyan transformation just like their male counterparts.