Some projects just can't succeed if project performers must always be asked to engage. Fast projects, innovation projects, and physically dispersed projects all cry out for 'jumping in.' How do you get more initiative and engagement? First, ask for it. But it is rarely enough.

Set an early example of taking initiative.
People may hold back 'til they've seen others in their group take part. Maybe this is an introvert thing, maybe not. But there's nothing like pointing to an example for calling for more engagement.

Make a game of it.
Share the rules (or guidelines) for play. Be clear how people win. Win? Sure. State clearly how 'jumping in' forwards the purpose of the project. If people see that, then they are more likely to take their first step. After a first step, there's bound to be a second.