You can! The timing is pretty tight, but it does forgive one mistake after the “run” cue. One advice to make it easier is to press the restart button (menu button on the left controller) if you miss a jump. Also try to jump forward and not up. You can also check out the full playthrough if you feel completely stuck: https://youtu.be/AIxQ8ZUeU1M
It is actually even possible to sequence break this level and complete it without pressing the space button, but it requires to make a really tough jump.