  Multi-wavelength extragalactic nuclear transients, particularly those
detectable as multi-messengers, are among the primary drivers for the
next-generation observatories. X-ray quasi-periodic eruptions (QPEs) are the
most recent and perhaps most peculiar addition to this group. Here, we report a
first estimate of the volumetric rate of QPEs based on the first four
discoveries with the eROSITA X-ray telescope onboard the Spectrum Roentgen
Gamma observatory. Under the assumption, supported by a suite of simulated
light curves, that these four sources sample the intrinsic population somewhat
homogeneously, we correct for their detection efficiency and compute a QPE
abundance of $\mathscr{R}_{{\rm vol}} = 0.60_{-0.43}^{+4.73} \times
10^{-6}\,$Mpc$^{-3}$ above an intrinsic average $\log L_{\rm 0.5-2.0\,keV}^{\rm
peak} > 41.7$. Since the exact lifetime of QPEs ($\tau_{\rm life}$) is
currently not better defined than between a few years or few decades, we
convert this to a formation rate of $\mathscr{R}_{\rm vol}/\tau_{\rm
life}\approx 0.6 \times 10^{-7} (\tau_{\rm
life}/10\,\mathrm{y})^{-1}\,$Mpc$^{-3}\,$year$^{-1}$. As a comparison, this
value is a factor $\sim10\,\tau_{\rm life}$ times smaller than the formation
rate of tidal disruption events. The origin of QPEs is still debated, although
lately most models suggest that they are the electromagnetic counterpart of
extreme mass ratio inspirals (EMRIs). In this scenario, the QPE rate would thus
be the first-ever constraint (i.e. a lower limit) to the EMRI rate from
observations alone. Future discoveries of QPEs and advances in their
theoretical modeling will consolidate or rule out their use for constraining
the number of EMRIs detectable by the LISA mission.
