What we can see is called the observable universe. We cannot see past that boundary. We don't know how big the actual full universe is. But, it is clearly larger than the observable universe.
So, all we can see is not in a snow globe because it is contained in the rest of the universe.
So, that part is trivial. You can then say, "Ok. I shall amend it to prove that the whole universe isn't a snow globe on God's desk."
Science's best model of the universe is that the universe started from the Big Bang, which was a quantum fluctuation that was special in that most such quantum fluctuations annihilate leaving photons. This isn't something from nothing. Rather, it is something from the quantum foam.
From there, Big Bang cosmology states that the early universe underwent a period of inflation, and so on. That explanation can be looked up in its entirety if one so desires.
The Big Bang Cosmological Theory explains what we observe better than anything else out there. To site one example, it explains the CMB--cosmic microwave background radiation. And, it explains a number of other things we have measured. These things can be looked up if one so desires.
There are other theories, to be sure. But, these other theories fall short on the explanatory power of the Big Bang. So, they have been shown the door, so to speak.
If another theory came along with equal explanatory power to the Big Bang, we would then use Occam's razor to decide which theory to discard (the theory with more assumptions is the one we discard).
And, if another theory came along that explained things better than the Big Bang or explained more things, then that new theory would replace the Big Bang theory.
This is how science works--it updates itself all the time as explanations and theories improve.
Now, as for the universe being in a snow globe on God's desk goes, this hypothesis does not have any explanatory power. So, it isn't even as good as the Big Bang model, which means we discard it immediately. There isn't even a need to use Occam's razor on it.