How can a non-physical God create a physical universe?

God is a Physical Being

God is not an non-physical being:

"The Father has a body of flesh and bones as tangible as man’s; the Son also..." (Doctrine and Covenants 130:22)

More about the nature of God Here.

God Organized Existing Matter to Create the Universe

God did not create matter:

“The materials out of which this earth was formed, are just as eternal as the materials of the glorious personage of the Lord himself. … This being, when he formed the earth, did not form it out of something that had no existence, but he formed it out of materials that had an existence from all eternity: they never had a beginning, neither will one particle of substance now in existence ever have an end. There are just as many particles now as there were at any previous period of duration, and will be while eternity lasts. Substance had no beginning; … the earth was formed out of eternal materials, and it was made to be inhabited and God peopled it with creatures of his own formation.” (Journal of Discourses, 19:286.)

This truth has also been discovered by scientists today who say that matter cannot be created or destroyed—only its form may be changed.

“In the Beginning”: A Latter-day Perspective

The Fulness of the gospel has been restored, and these questions, along with many others, have been answered by modern prophets who continue to receive revelations about God's will and guide us in these latter-days.

You appear to be making the most prevalent misconception that people make.

That misconception is that the physical realm is the true realm, while in truth it is the Spiritual realm which is predominant. Just so that I do not confuse you let me explain things this way. The physical realm exists in the Spiritual realm. By that what is meant is that the Spiritual realm(or if you prefer the Realm in which God exists.)is an eternal Realm meaning that it has no beginning and no end.

The physical realm on the other hand has both a beginning and an end. All Scientists agree that the universe (or if you will the physical Realm) began at some point in the past, even though there is wide disagreement on both how and when. The most prominent view is the Big bang theory in which the Universe came into being almost instantaneously from the same point in Space from one extremely large and powerful explosion. To me that pretty well describes creation.

All things material have a beginning and an end. that even applies to boulders in that over sufficient time the environment will break the boulder down into smaller rocks. I have personally seen a large rock broken into two pieces by water freezing and expanding.

If the idea of a Spiritual realm is difficult for you to visualize consider this how far does space extend? If Space does not go on without end, the what would be outside of Space and would that also end and so on to infinity.

Indeed Space itself may in fact be the Spiritual realm, and that makes the following Scripture make sense:

MarK 16:19 So then after the Lord had spoken unto them, he was received up into heaven, and sat on the right hand of God.

Whatever the case only some power beyond anything our human mind can imagine has to be responsible for all things material at some time in the past, being created from nothing even if it were one tiny atom.

Your question is a creative one and as humans we tend to think in human terms.

In our day however we have a greater capacity of understanding how such things could even be possible.

I'm going to use the example of computer games as what might be a humanly relatable comparison. I'm usually not one to use elaborate world-oriented illustrations, but this time I will.

Think of a programmer, and a computer. Perhaps even a game, with a character in it.

The environment is completely virtual, and yet its perfectly possible for it to reflect any system or idea the programmer may wish to present. On a very simple level we can emulate reality through a game, or even invent our different realities. We can interact with it through a window (monitor or television), and yet even that requires a high level of abstraction and visualization.

If humans can do this with a machine, we could even present the idea that we are ourselves in an environment created by a master programmer, complete with laws of cause and effect, intelligent characters locked into the game, and even characters separate from it, controlled from the outside. Our human characters have the capacity to experience the world in pre-programmed ways through our senses (and really, our senses are just translators for environmental events, which are little more than information).

This idea is not too far fetched:

Psalm 139:16

Your eyes saw my unformed body; all the days ordained for me were written in your book before one of them came to be.

Some believe this could even loosely refer to matters of DNA, but it implies a design by a higher authority on both events and physical matters.

Luke 10:20

However, do not rejoice that the spirits submit to you, but rejoice that your names are written in heaven."

Luke 12:7

Indeed, the very hairs of your head are all numbered. Don't be afraid; you are worth more than many sparrows.

You can look through a technological window (the television or monitor) and see the character's gaming world just how it should be perceived. We could speculate that the spiritual realm (where God himself resides) can see us the same way, and even interact with it, the same as many might interact in an online game. Thus we have stories of angels materializing, and things such as miracles (and even sorceries)...created by higher beings who understand the programming, and even have the capacity to exploit it for better or worse.

Creation is in a way a giant program of cause and effect, the programming of which we ourselves know we can alter. Thus even in the bible, you have the stories of the nephilim: Genesis 6:4 where wicked angels corrupted God's creation to an extreme.

So from even our human understanding shows that its perfectly possible to create one realm from another realm as in my gaming example.

Origin of physical matter...

In my personal opinion its easier to picture the creation of a physical realm from a spiritual realm, than a spiritual realm from a physical one.

We know that God resides in a source of light so powerful it can't be approached:
1 Timothy 6:16

who alone is immortal and who lives in unapproachable light, whom no one has seen or can see. To him be honor and might forever. Amen.

By way of comparison today, we know that when matter decays it takes the form of electromagnetic radiation, and we know light is a visible spectrum of electromagnetic radiation. So we know that the source of matter is energy (we could loosely refer to as "light"), and we know that God is the source of energy itself, and is often associated with light.

Even modern day "big bang" theory has energy as the dominant player, creating the rest of the physical world and reality we know. So its not hard to put an intelligent director (and source) behind that energy that defines our universe.

And yet our universe we can see is only a small part of the bigger picture:

26:14 - Behold, these are but the outskirts of his ways, and how small a whisper do we hear of him! But the thunder of his power who can understand?”