According to classical electromagnetic theory, which describes the behavior of electromagnetic waves, the electric and magnetic fields in an electromagnetic wave are intrinsically linked and propagate together. They are in phase with each other, meaning they reach their maximum and minimum values at the same time and at the same location.
The concept of the birth of a photon is more closely associated with quantum mechanics, which describes the behavior of particles at the microscopic level. In quantum mechanics, a photon is considered as a quantum of electromagnetic radiation, and it is described by a wavefunction that evolves over time.
In the quantum mechanical description, the wavefunction of a photon includes information about the amplitude and phase of the electric and magnetic fields. However, it is important to note that the electric and magnetic fields of a photon are not independent entities but rather different aspects of the same underlying electromagnetic field.
In this context, there is no notion of an infinitesimally small time difference or phase difference between the electric and magnetic constituents of a photon at its birth. The electric and magnetic fields of a photon are intimately connected and evolve together in a coherent manner.
It's worth mentioning that in certain exotic scenarios or under extreme conditions, such as in the presence of certain types of media or in high-energy physics experiments, there can be phenomena that involve deviations from the classical electromagnetic wave behavior. However, these are specialized cases that generally do not apply to everyday observations of light and electromagnetic waves.