No, it is not possible to go to Sundarbans by car as the forest is located in a remote area and can only be accessed by boat. The nearest roadhead is Godkhali, which is about 110 km from Kolkata and is the starting point for most Sundarbans tours. From Godkhali, visitors have to take a motorized boat to reach the forest.
It is recommended to hire a car or taxi from Kolkata to reach Godkhali, as it is a long journey that takes around 3-4 hours. Once you reach Godkhali, you have to park your vehicle and continue the journey by boat.
Therefore, while it is not possible to go to Sundarbans by car, you can still hire a car or taxi to reach the nearest roadhead and then continue your journey by boat to explore the mangrove forests and its wildlife.