Earth's early rise in oxygen, known as the Great Oxidation Event (GOE), remains a fascinating and complex phenomenon in the evolutionary history of life. The role of oxygen during this period is still a subject of ongoing research and scientific debate. There are arguments both in favor of the idea that the rise in oxygen supported the evolution of multicellular life and for the notion that it initially posed challenges, leading to possible suppression.

1. Supportive Arguments

a. Aerobic Metabolism: The rise of oxygen allowed the evolution of aerobic respiration, a far more efficient metabolic pathway compared to fermentation. This energy boost supported larger body sizes and increased complexity.

b. Oxygen as a Signaling Molecule: Oxygen could have acted as a signaling molecule, regulating cellular processes, growth, and development, thus influencing the emergence of multicellular life.

c. Oxygen as a Protective Agent: Oxygen has antioxidant properties and can help mitigate oxidative stress. It could have protected early life forms from damage caused by free radicals.

d. Ecological Opportunity: Increased oxygen levels could have influenced environmental conditions, leading to the availability of new niches and resources, thereby driving evolutionary adaptations.

2. Challenging Arguments

a. Oxidative Stress: On the other hand, oxygen is a highly reactive element, and elevated levels can cause oxidative stress, damaging cellular structures and components. This could have had detrimental effects on early life forms.

b. Transitional Challenges: The transition from anaerobic to aerobic metabolism could have been a challenge, requiring evolutionary innovations to cope with the new conditions.

c. Environmental Shifts: The rapid increase in oxygen levels could have disrupted some stable ecosystems, potentially leading to extinctions or population declines.

d. Late Emergence: Some studies suggest that multicellular life emerged millions of years after the GOE, which might imply that oxygen was not an essential prerequisite.

In summary, the rise of oxygen during the GOE had both supportive and challenging effects on the evolution of multicellular life. While oxygen provided energetic advantages and opened new ecological niches, it also posed new problems in the form of oxidative stress and transitional difficulties. The intricate interplay of these factors shaped the trajectory of early life's evolution and continues to be a subject of ongoing research and scientific exploration.