During the Episode 1 prologue, is it possible to not fall from a branch?

During the Episode 1 Prologue, you fall off a cliff and grab a tree branch. This results in a quick-time event where you have to press the same button repeatedly to avoid falling. However, whenever I try, the branch breaks before the meter is full.

Is it possible to press one of the buttons fast enough to avoid falling, or is the falling part unavoidable?

The falling part is unavoidable. While playing on the Steam version, I used my controller's turbo mode and still fell. There is also no achievement for preventing the fall. The fall also has no impact on obtaining any of the achievements.