No, as an observer, you cannot see photons traveling away from you directly. Photons are particles of light that travel at the speed of light. When photons reach your eyes, they interact with the cells in your retina, triggering a series of biochemical reactions that eventually lead to the perception of light. However, this process involves photons entering your eyes and interacting with the light-sensitive cells, not observing photons themselves as they travel.
Photons are not typically visible unless they interact with matter or are absorbed by certain substances, such as fluorescent materials. For example, when photons strike an object and bounce off, they may then enter your eyes and be detected as reflected or scattered light, allowing you to see the object.
In essence, you perceive the effects of photons when they interact with objects or when they are emitted or reflected by objects and enter your eyes, but you do not directly see photons themselves as they travel through space.