Can science tell us "what God is like?" I don't see why not. All truth emanates from and speaks to the One Truth, so there's no reason why science should be any different, so long as we don't try to reduce God to what can be expressed scientifically.
Rather, science can provide a "view of God," so to speak (just as it provides a view of matter, or life, or stars, or whatever else it looks at).
Scripture tells us that man is created in the image and likeness of God. Now, man is clearly the most astonishing fact in all of existence, so it makes sense that this most unique and unusual being -- man -- is said to mirror the Absolute Principle underneath the whole existentialada.
Now, what are some of the unique features that define this unusual creature, man?
There are many to choose from, including,
I would add that although we cannot know them in their fullest sense, we can certainly intuit timelessness, infinitude, and absoluteness, or in other words, touch the divine qualities of nonlocality, omnipresence, omniscience.
What are the chances? I mean, what are the odds of a randomly evolved being just happening to develop one of these divine traits, let alone all of them?
Indeed, it seems to me that they must come as a package deal, such that we can't have one without the others.
For example, truth is inconceivable in the absence of freedom, and vice versa (i.e., freedom without truth is just another name for meaninglessness, or absurdity, or being lost in the cosmos).
Likewise, knowledge is a priori transcendent, as is disinterested love, or reason, or freedom, and I don't see how we can ever get off the genetic arbitrary goround in the absence of an intersubjectivity that allows us to understand and communicate inner and outer reality.
It seems to me that it must all come down to the Trinitarian nature of God. For if God were... mono- or duo-tarian, then man -- and the cosmos -- would appear much different than they do.
For example, if God is a radical monad, there is no one to love, nothing to know, no one to give back to, etc. You know the old gag:
But it was not good that this Godhead, the Most High, should be allone... Indeed, this old ombody's so philled with jehoviality, can't He create anamour?
In fact, he can't stop (creating, loving, knowing, etc.).