There are two different things described by the word 'Universe'.
The first - more frequently used by mathematicians than natural scientists, as far as I know - means, roughly, 'all that can be', including things that, for instance, are not considered within 'existence' (which is a proper subset of the Universe) at some specific point in time, but can exist, given a particular set of variables.
The second, sometimes called the 'observable universe', is the collection of everything that can be said to exist for a particular set of coordinates in the various dimensions.
Things may 'randomly, spontaneously pop into existence out of nothing' in the second sort of universe, but not the first.
I am talking about the physical universe, not some abstract concept. Also, be careful when you say "observable universe", because the observable universe is a subset of the entire universe. It is the part of the universe, with Earth at its center, that we're
capable of observing, due to the limitation that nothing can travel faster than the speed of light. See
this if my explanation makes no sense.
Correct and from what we can see so far, it appears nothing is just popping into existence, but rather being created from other materials that already existed.
There's this thing called the
Casimir effect. I don't know too much about it, but I think it's basically a force that arises, out of nothing, between two neutral electrically conductive plates in vacuum. In vacuum, "virtual" photons do in fact randomly pop in and out of existence due to quantum fluctuations. The virtual photons between the plates are quantized due to them being in a confined space, while the virtual photons everywhere else are not. In a sense, there are "more" virtual photons outside the plates than inside, so the plates are pushed toward each other. If my explanation makes no sense, watch
this video. Yes, this thing has been experimentally verified.
My point is that things do actually pop into existence out of nothing. True, you don't see them in everyday life, but that doesn't mean they're not there. Because of this, I'm not denying the possibility that the whole universe just randomly popped into existence out of nothing. If God created the universe, then where did God come from? Saying that God is beyond the concept of beginnings and ends is unfalsifiable, so I won't even bother with it.