Is the following true?
The only matter existing directly after the big bang was electromagnetic radiation.
We don't know what happened in the very early stages of the Big Bang because we have no experimentally tested theory that takes us back that far. However, courtesy of the LHC we have an experimentally tested theory that takes us back to a time called the electroweak epoch, and we can use this theory to answer your question in the negative.
Electromagnetism is a low energy effective theory. It works below energies of somewhere around a teraelectron volt, but above that energy it has to be replaced by a unified theory of the electromagnetic and weak forces called (somewhat obviously) the electroweak theory. The discovery that proved this (not that anyone seriously doubted it) was the discovery of the Higgs boson at the LHC in 2013.
Anyhow, the electroweak theory tells us that during the electroweak epoch there were four massless vector bosons. At low energies these become the Z, W$^+$, W$^-$ and the photon, but above the electroweak transition the four bosons were indistinguishable.
I confess I don't know how to calculate the particle content during the electroweak epoch, so I shall say nothing further on the subject. Nevertheless we can be confident that whatever was floating around at those energies was not just photons.
I could start by saying that this depends on what your definition of the big bang is, but that would be pointless because the better question is how do you define matter? Or "directly after"?
Firstly, let me say the technical answer is no because electromagnetic radiation is not matter (in a cosmological context). But I assume that the quote meant the only type of energy. If that's the case, the answer is still no because dark energy existed at that time too. It's also possible the quote means to just say that there was no baryonic matter, which is true. If the quote meant there was no particles of any kind save photons, then that is both silly and false. Directly after the big bang, there were also gravitons and dark matter and other force mediating particles and some fundamental particles. At the time of the big bang (again depending on your definition of it), the energy scale was too high to be described by modern physics accurately, so it's tough to say. Some models have a universe where photons didn't even exist until a fraction of a second into the hot big bang era.
But the answer to what this question is most likely asking is no.
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