How can a photon be a wave and a particle at the same time?

It is a quantum object. Early 20th-century experiments forced physicists to give up on the traditional idea of a particle as a solid object; instead, particles behave like waves in a probabilistic sense. The particle is now universal and no longer localized; fields are also quantum, and the photon is nothing more than the energy unit of an electromagnetic field.

There is no short answer to any question, including mine, so please read as much as you can. Books like QED can be helpful. Keep asking.

A fundamental aspect of quantum mechanics that is supported by experimental evidence is the concept that a photon can behave as both a wave and a particle. This is known as wave-particle duality, which states that particles, like photons, can exhibit characteristics of both waves and particles depending on the experimental setup and observation method. In light-based experiments, photons often behave like waves, exhibiting phenomena like interference and diffraction; however, they can also behave like particles, as seen in the photoelectric effect, where individual photons interact with matter as discrete entities, transferring their energy in quantized amounts.