Actually, the mechanism of $\ce{Ag3N}$ creation (and also the associated products, silver amide $\ce{AgNH2}$, and the imide $\ce{Ag2NH}$), have not been definitely accounted for, either by accident investigation reports or per a recent review of the literature, on possible paths to explosive Silver nitride.
I have ideas of a wider chemistry spectrum based answer which accounts for the apparent role involving $\ce{Ag2O}$.
To begin, I cite the more common background description, per a government source, to quote:
Silver nitride is an explosive chemical compound with symbol $\ce{Ag3N}$. It is a black, metallic-looking solid which is formed when silver oxide or silver nitrate is dissolved in concentrated solutions of ammonia, causing formation of a silver-amide or imide complex which subsequently breaks down to $\ce{Ag3N}$.
So, of interest is the cited reaction:
$\ce{Ag2O(s) + 4 NH3 + H2O ⇌ 2 [Ag(NH3)2]OH}$
where I would expect any silver oxide formed from the reverse reaction of dissolving $\ce{Ag2O}$ in ammonia would then likely create a high surface area (with enhanced reactivity) $\ce{Ag2O}$. It should also importantly be noted that the reaction, itself, is reversible (see as a source, "Second year college chemistry" by William Henry Chapin, page 255), to quote:
As might be expected, the silver-ammonium complex dissociates slightly into its constituents as indicated by the equation
$\ce{[Ag(NH3)2]+ ⇌ Ag+ + 2 NH3}$
This is a reversible reaction, very much like the ionization of a very weak acid or base.
So, once any $\ce{Ag2O}$ is formed (by say moving the equilibrium to the left from a possible loss of water on standing in an open vessel or upon addition of dry alcohol), a radiation source could further accelerate the process (see, for example, $\ce{Ag2O}$ as a New Visible-Light Photocatalyst: Self-Stability and High Photocatalytic Activity). To quote from the abstract:
$\ce{Ag2O}$ is unstable under visible-light irradiation and decomposes into metallic $\ce{Ag}$ during the photocatalytic decomposition of organic substances. However, after partial in situ formation of $\ce{Ag}$ on the surface of $\ce{Ag2O}$, the $\ce{Ag2O}$-$\ce{Ag}$ composite can work as a stable and efficient visible-light photocatalyst.
As such, the introduction of appropriate light, or other irradiation paths (like X-rays commonly associated with radical formation) may be instrumental. In fact, here is an interesting pertinent radiation study: The X-ray activated reduction of silver (I) solutions as a method for nanoparticles manufacturing. To quote from a passage discussing an associated radiation treatment:
The next step was aimed at eliminating glucose-containing ammonia solutions. The reactions taking place in these solutions resulted sometimes in the formation of precipitates with unstable composition. These precipitates contained considerable amounts of silver nitride $\ce{Ag3N}$, which formed in some ammonia solutions of the silver salts and exhibited explosive properties in a dry state [15]. The results from analysis of the deposits obtained for three selected types of solutions are presented in Table 1.
As the irradiation of glucose is a path to radicals, my proposed mechanics incorporates an ostensible promotive radical pathway for the allude to creation of $\ce{Ag3N, Ag2NH and AgNH2}$, which also appears to be accelerated in the presence of $\ce{OH- and Ag2O}$ in the presence of ammonia.
The proposed reaction path is:
$\ce{NH3 + H2O ⇌ NH4+ + OH-}$
$\ce{NH4+ ⇌ NH3 + H+}$
$\ce{[Ag(NH3)2]+ ⇌ Ag+ + 2 NH3}$ (per above)
In the further presence of light:
$\ce{Ag+ + hv -> •Ag + h+}$
Source: See Photodecomposition and Luminescence of Silver Halides
$\ce{OH- + h+ -> •OH + hv}$ (same source as above)
$\ce{OH- (aq) + hv -> •OH + e- (aq)}$
As a reference, see: Flash photolysis in the vacuum ultraviolet region of sulfate, carbonate, and hydroxyl ions in aqueous solutions
$\ce{NH3 + •OH -> •NH2 + H2O}$
From a related work: Kinetics and Mechanism of the Reaction of •NH2 with O2 in Aqueous Solutions
$\ce{NH3 + •H <=> •NH2 + H2}$
As noted in this work.
$\ce{•NH2 + e- -> NH2-}$
$\ce{Ag+ + NH2- <=> AgNH2}$
$\ce{2 AgNH2 -> Ag2NH + NH3}$
$\ce{AgNH2 + Ag2NH -> Ag3N + NH3}$
Note, my suggested pathway is largely promoted from the recognition of $\ce{Ag2O}$ as a recent (article was 2011) visible-light photocatalyst with the possible introduction of contributing radical based reactions.
In summary, I am suggesting chemically diverse mechanisms, involving both light and radical based reactions, as a more likely explanation.