It Is Possible to Create Protons from Photons?

Yes. This is possible from colliding real photons (i.e., on-shell photons).

Protons (p$p$) are composite particles composed of three quarks: two up quarks (u$u$) of charge +2/3$+2/3$ e$e$ and one down quark (d$d$) of charge −1/3$-1/3$ e$e$. While, anti-protons (p¯$\overline{p}$) consist of two up antiquarks (u¯$\overline{u}$) of charge −2/3$-2/3$ e$e$ and one down antiquark (d¯$\overline{d}$) of charge +1/3$+1/3$ e$e$. So, in principle, production of pp¯$p\overline{p}$ is allowed in γγ$\gamma \gamma \; (gamma\; gamma)$ collisions. 

This can be understand by the following Feynman diagram :

The quark-quark-photon and antiquark-antiquark-photon vertices in the above diagram can be understood using electromagnetic interactions such as QED. The process will lead to the formation of a pp¯ pair if the initial collision $\gamma \gamma$  has enough energy to produce a proton-antiproton pair. Three quarks (two u quarks and one d quark) and three antiquarks (two u¯ antiquarks and one d¯ antiquark) are needed for this. As a result, we need Feynman's diagrammatic expansion:

According to the allowed vertices in electroweak and QCD theories (in the Standard Model of elementary particles), the dashed part of this diagram contains an infinite number of terms . There are three vertices in QCD. One of the simplest Feynman diagrams is as follows:

or

It's worth noting that the four possible vertices are applied, as follows:

We now have three quarks (q) and three antiquarks (q¯$\overline{q}$). Supposing that two of quarks are u$u$ quarks and one of them is d$d$ quark, and supposing that two of antiquarks are u¯$\overline{u}$ antiquarks and one of them is d¯$\overline{d}$ antiquark. 

The three quarks hadronized into proton, and the three antiquarks hadronized into anti-proton in the end. In a number of studies, this process has been confirmed experimentally and analysed. In conclusion, photons can be used to make protons (together with anti-protons).