Yes. This is possible from colliding real photons (i.e., on-shell photons). I try to show you how this is possible within the context of Standard Model of elementary particles.
Protons ($p$) are composite particles composed of three quarks: two up quarks ($u$) of charge $+2/3$ $e$ and one down quark ($d$) of charge $-1/3$ $e$. While, anti-protons ($\bar p$) consist of two up antiquarks ($\bar u$) of charge $-2/3$ $e$ and one down antiquark ($\bar d$) of charge $+1/3$ $e$. So, in principle, production of $p \bar p$ is allowed in $γγ$ collisions. This can be visualized by the following Feynman diagram (hereafter, $q$ stands for quarks and $\bar q$ for antiquarks):
In the above diagram, the quark-quark-photon and antiquark-antiquark-photon vertices can be understood via electromagnetic interaction like QED. If the initial $γγ$ collision has enough energy for producing a proton-antiproton pair, then the process can lead to the production of a $p \bar p$ pair. For this purpose, we need three quarks (two $u$ quarks and one $d$ quark) and three antiquarks (two $\bar u$ antiquarks and one $\bar d$ antiquark). So we need such a Feynman's diagrammatic expansion:
The dashed part of this diagram consist of infinitely many terms according to the allowed vertices in electroweak and QCD theories (in the Standard Model of elementary particles). In QCD, there exist three vertices and I restrict myself here to QCD interactions. For example, one of the lowest Feynman diagrams can be illustrated as
Another example is this one:
Note that, I've implemented the four possible vertices (within QED and QCD) in this answer, summarized as
Now, we have ended up with three quarks ($q$) and three antiquarks ($\bar q$). Supposing that two of quarks are $u$ quarks and one of them is $d$ quark, and supposing that two of antiquarks are $\bar u$ antiquarks and one of them is $\bar d$ antiquark, finally, the three quarks hadronize into proton and the three antiquarks hadronize into anti-proton. This process has been confirmed experimentally and analyzed before in a number of studies. In conclusion, it is possible to create protons (with anti-protons) from photons.
You may also find the following (relevant) studies/papers useful:
L3 Collaboration, "Proton–antiproton pair production in two-photon collisions at LEP", Phys. Lett. B 571, 11 (2003), arXiv:hep-ex/0306017.
M. Kłusek-Gawenda, P. Lebiedowicz, O. Nachtmann, and A. Szczurek, "From the $\gamma\gamma\to p\bar p$ reaction to the production of $p\bar p$ pairs in ultraperipheral ultrarelativistic heavy-ion collisions at the LHC", Phys. Rev. D 96, 094029 (2017), arXiv:1708.09836.
TASSO Collaboration, "Exclusive proton-antiproton production in two-photon collisions." Phys. Lett. B 108, 67 (1982).
VENUS Collaboration, "Measurement of the proton-antiproton pair production from two-photon collisions at TRISTAN." Phys. Lett. B 407, 185 (1997).