It is going to be difficult for conventional levels of spheres to do that. Fortunately, the book Masters of the Art deals with high levels spheres (up to 9); on page 73 you have the 9th level of Prime as literally create a universe:
An Archmage at the pinnacle of Prime can also use Quintessence to
create a pocket universe. The internal dimensions of this universe,
and all other properties, are at the Archmage’s discretion; his
knowledge of Patterns is the only factor limiting the universe’s
internal properties. This pocket universe is a small piece of folded
space where the Tellurian naturally balls itself off in a sort of
protective shell. Naturally, watching this universe evolve can provide
all sorts of insights for less-experienced fledgling mages, and it may
even be an interesting place to visit for the Archmage creator. The
mage simply gives the tiny Pattern a spark of creative force, and lets
it run. Perhaps this is the way our own universe started...
As for the information transfer, that is usually Correspondence, although I am not sure to what degree you will need it to transfer a whole universe's worth of information (you will get some Virtual Adepts really interested here). But since we are already with arch-spheres, we could probably think of something like Correspondence 8: Limits of Spirit (on page 67):
Since the mage can easily create bubbles of space that share
characteristics with other space — essentially co-locating spatial
features instead of just objects [...]
The question “will that be enough?” is a good one, since, well, it is not stated that life exists on that new universe or any kind of matter. I it unclear if you will need to “put that in” so to say (but then again, does time exists in this new dimension? Do you need that? Does this universe have an Umbra if I do not use Spirit? And so on...)
As usually with Mage, my best guess is “depends on your Narrator’s interpretation”.