Generally virtual particles they don't 'pop into and out of existence'...nobody has ever detected that actually happening...it's an introductory illustrative way to think about more complex mathematics. One way such imaginary events might happen is when gravity yanks particles apart at a horizon [see below].
here is a better way to think about particle production...given a quantum field, say an idealized free electron not interacting...it's a field, you can't observe it...Now confine that field inside an event horizon, or capture that electron around a nucleus...it is confined when 'captured'...it resonates...it is finite in extent...it is a detectable particle! Analogous to wiggly violin string: clamp the ends, tighten it perhaps, it now resonates at certain frequencies...
and here is an even better description:
I think I got this from Wikipedia...wherever, I like the description:
..There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. As such, virtual particles are also excitations of the underlying fields, but are detectable only as forces but not particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modeled. In this sense, virtual particles are an artifact of perturbation theory, and do not appear in a non-perturbative treatment...
On the other hand, even Stephen Hawking used a description of virtual particles separating at a black hole horizon to 'illustrate' Hawking radiation...although it had nothing to actually do with his mathematical calculations. The 'real; particle escapes to be observed.
Also, it is worth noting quantum FIELDS, extended versions of particles, that expand in space with expanding space can become 'particles', which we describe as quanta [localized versions] of fields...what we detect. There are a variety of ideas about how this might happen.
One way is via cosmological inflation: a dynamic spacetime geometry, like cosmolgicial inflation, can turn quantum fluctuations [ that we observe in the cosmic background radiation all around us] into particles at vast horizon scales. In other words, a changing, dynamic, spacetime geometry associated with event horizons produces real [observable] particles. Event horizons might be cosmological, black hole or Rindler type in Unruh radiation.
edit: for more, search "virtual particles" in these forums...and
Particle creation in an accelerating Universe?
https://www.physicsforums.com/showthread.php?t=590798&page=2
