There are few good options for parking near the trailhead. Parking is not free and you should avoid parking on the public road due to high volume of traffic. Most of the listed parking charges $2,000 pesos per day.
The owner Claudio, born and raised in Cochamó, was the first house on the block and is the primary place to park. His kind nature, willing to help and spacious area makes a good place to leave your vehicle.
Another locally run and owned camping and parking. Located just before the previous parking / camping, it offers or more isolated feel to the rest of the busy trailhead area.
This is about 600 metros from the trailhead but if you need a place to stay combined with proximity to the trailhead, this is a great option.