ExcellentCrates

When ExcellentCrates is installed, the excellentcrates_crate_open trigger becomes available. Detection is automatic.

Trigger	Counts when the player...	Progress
excellentcrates_crate_open	opens a crate	1 per opening

The target is the crate's ID (the config/file name in ExcellentCrates, not the display name). Use any or all to count every crate:

objectives:
  lucky_day:
    name: "&#FFD86E&lLucky Day"
    description:
      - "&#C7D0D9Open epic crates and test"
      - "&#C7D0D9your luck."
      - ""
      - "&#8A8F98Progress: &#FFFFFF{progress}&#8A8F98/&#FFFFFF{required}"
    trigger: excellentcrates_crate_open
    target: epic
    required: 3

Or, counting any crate:

objectives:
  crate_hunter:
    name: "&#7CF6FF&lCrate Hunter"
    trigger: excellentcrates_crate_open
    target: any
    required: 10

A crate-open quest pairs nicely with a crate-key reward — a quest that opens crates and pays out a key for a better one gives players a reason to keep both systems running:

rewards:
  - type: command
    display-name: "&#FFD86E1x Epic Key"
    value: crates key give %player% epic 1