Wondermine said:
The reason I used the word singularity is that there was only one event referred to (the "bang") and that the degrees for freedom would be minimal as in a singularity.
The term "Big Bang", properly interpreted (i.e., as cosmologists actually use it, as opposed to pop science usage), does not refer to any "initial singularity". It refers to the hot, dense, rapidly expanding state that is the earliest state for which we have good evidence. The current majority belief appears to be that this state occurred at the end of an inflation epoch, but that is still, strictly speaking, an open question.
Thinking of the correct "Big Bang" state as having minimal degrees of freedom is not a good way to think of it. Because of the extremely high temperature, that state actually had many
more degrees of freedom excited (i.e., containing significant energy density) than our universe today does.
Wondermine said:
The reason I thought that there would be no photons is that under extremely (most extreme) confined degrees of freedom there would not be room enough for a whole photon wavelength.
Wavelength depends on energy; the higher the energy the shorter the wavelength. At high temperature most of the photons will be very high energy and therefore very short wavelength.
Also, this argument, if it were correct, would prove too much: it would prove that there could be no particles at all at high temperature, since they all work the same as photons do as far as wavelength is concerned.
Wondermine said:
the wavelengths and frequencies being so tiny they would more properly be forces,not photon waves. I then imagined that only force fields would be present and the candidate being the Strong Force as being the smallest and tightest form of atomic energy
This is not a good way to think of it. The distinction between "force fields" and "waves" is not a matter of how small the wavelengths get (btw, small wavelength means very
high frequency, not low). In fact, if anything, smaller wavelengths (and higher frequencies) are more likely to have "wavelike" behavior than "force field like" behavior; what we usually think of in everyday life as "force fields" are manifestations of quantum fields at long wavelengths and low frequencies and therefore low energies (and also off the mass shell as opposed to on shell, but that's a whole separate can of worms). When wavelengths get very small (and frequencies/energies get very high), the behavior gets more "particle-like", e.g., what is seen in high energy experiments like the LHC. Those experiments have no useful features in common with "force fields"; the best quick layman's description is that they're very high energy particles hitting each other and breaking into various pieces.
Wondermine said:
This then lead to the question about how atoms could be formed if rapid expansion occurred given the Strong Force acts over a tiny distance only.
As you should be aware by now, this question is based on a number of misunderstandings. When the misunderstandings are cleared up, the question vanishes. To quickly recap: when atoms were formed, the universe was at a much lower temperature than a quark-gluon plasma would be, and the dominant forces were gravity (governing the large scale expansion of the universe) and electromagnetism (which is what attracted electrons to nuclei to form the atoms). The strong force had already done its major job a long time before, by driving nucleosynthesis in the first few minutes of the universe--and even that was well after the quark-gluon plasma stage. When the strongly interacting portion of the universe's energy density was a quark-gluon plasma, the temperature was much too high for any higher level structures at all to form--not even protons or neutrons, much less nuclei or atoms. And even at that time, the quark-gluon plasma was not the only significant component of the universe: others included electrons and positrons, neutrinos and antineutrinos, W and Z bosons, and photons.