Final answer:
The Commanding Officer's recommendation is generally considered the most critical factor for advancement to E-4 in the military, as it is a significant endorsement of the service member's potential for increased responsibility.
Step-by-step explanation:
When it comes to the advancement to E-4 in the military, each of the elements you listed plays a significant role. However, among them, the Commanding Officer's recommendation is often considered most crucial for career progression. While time in rate and professional military knowledge are important qualifiers, and passing the advancement exam demonstrates a service member's competence, the Commanding Officer's recommendation carries considerable weight as it is a testament to the individual's character, reliability, and suitability for increased responsibility. Such a recommendation can sometimes be seen as a seal of approval that encompasses and validates the other requirements.