Carpool in Puerto Natales

Hey, I'm planning visiting purto natales in the mid to end of abril next year. My permanent drivers license wont be ready to rent a car in the time of the vacation. When i was looking at the time the bus from puerto natales arrive at torres del paine, i began to realize that it wouldn't fit my itinerary.

It's safe to try carpool in the road to puerto natales? I'm a bit worried that in the end of abril that wont be so many cars and I mght arrive at the same time of the bus. Do you guys think it's worth it and safe to try and carpool? (I'm thiking of going on the road around 5:45/6 am.

Can someone help me?