If there is no God, we don’t make sense,
What, in your view, is the linkage between "God" (however you define that) and "making sense?" As far as I can tell, we make as much sense as any other organism or class of objects in Universe. How, in your theistic cosmology, does a Vampire Squid "make sense?" How about Toxoplasma gondii
? Tau Ceti?
The unspoken premise of this question is that humans need some sort of external authority to impose
"sense-making" upon them. You have provided no evidence or argumentation indicating why this should be so. Even if that were the case, what about "God?" If your concept of "God" happens to be within the conceptual ballpark of the anthropomorphic monotheisms (Judaism, Christianity, Islam) in which "God" is said to be a male personal entity with humanlike thoughts, emotions, desire for status and power ("King of kings and Lord of lords!") and so forth, and his authority is needed to impose things like "sense-making," morality, purpose, and so forth upon us, then your model only kicks the problem back a step. Who decrees that "God"
"make sense?" Who gives "his"
life meaning and purpose? How can "God" have morality, without a Moral Lawgiver to impose it on "him" from above?
The usual answer--that things like "making sense," meaning, purpose, and morality derive from "God's" nature--may be applied with far greater logical validity to human beings. For example, take the common moral injunction forbidding theft. "God" is usually said to, in some sense or other, "own" the Cosmos and everything in it. I do not know of any theological viewpoint in which it is considered metaphysically possible for a capital-g "God" to steal anything. Nor would it be possible (apart from metaphor) for anyone or anything to steal from "God." Even if someone could somehow steal, say, the Andromeda Galaxy from "God," "God" is not in any sense harmed. How can a prohibition against theft derive from "God" when it isn't even applicable to such an entity?
The concept of "theft" arises in a specifically human context. Humans need or want material things (farmland, money, a television) that can be taken from them by other human beings, and this action results in harm to the victim. Thus, a prohibition against theft makes sense in a human context, but does not make sense in a monotheistic context of "God."
You can go down any list of moral precepts you choose and encounter the same situation; likewise for concepts like "purpose," "meaning of life," and so on.
So, we have no reason to link any notion of "God" to the question of whether humans "make sense" or not.
so how do we explain human longings and desire for the transcendent?
First of all, I would have to say that genuine longing and desire for the transcendent (however defined) appears to be fairly rare among humans. Mysticism is a lot of work. It requires considerable time and sacrifice. Most people are not willing to give up their car and television (or their farm and oxen in pre-industrial times)--not to mention things like beer, sex, or nice clothes--to live in a monastery contemplating the transcendent. Or (in a secular scientific context) pursue a degree in astrophysics, mathematics, or physics so that they can dedicate their lives to probing the mysteries of Universe.
How do we even explain human questions for meaning and purpose, or inner thoughts like, why do I feel unfulfilled or empty?
The primary method of survival for humans is tool-making. Whether you're talking about a Clovis point or a cyclotron, tool-making involves the act of adapting available resources to serve teleological ends. We make a tool to serve a particular purpose. While some animals do make and use tools, they do not do so in the wide-ranging way that humans do, and their survival is not wholly dependent on tool-making as ours is. Humans have a natural tendency to look at Universe through human-colored glasses.
We tend to "see" human-like sapience where it does not exist.
Since we survive by making things "for" various purposes, it is not a great leap to expect that we would look at Universe and ourselves and wonder, "What for
Why do we hunger for the spiritual, and how do we explain these longings if nothing can exist beyond the material world?
Again, genuine "hunger for the spiritual" sufficient to motivate a person to actually cultivate mystical experience (spending an hour a day in meditation/tai chi/yoga/Thelemic magickal practice/whatever, monastic life, expensive and/or difficult pilgrimages to sacred sites, etc.) is fairly rare. Most religious people are content to substitute unquestioning acceptance of the second-hand dogma of clerical institutions (usually the ones that just happen to be prevalent in their local culture) for any sort of "spiritual quest." This common religiosity usually serves other purposes to a greater degree: community-building, provision of mutual support and charitable aid, tribal identification, a communal moral framework, the ego-gratification that comes with being a member of the One True Faith, a framework for status-seeking and/or finding an Authority to submit to, etc..
Your question also founders on the assumption of a duality between "the spiritual" and "the material world." A neutrino can shoot through Planet Earth at the speed of light as if Earth isn't even there. Is the neutrino "material?" Certain mushrooms that can be weighed on a scale or dried, ground up, and placed in a test tube, can generate profound mystical experiences when ingested. For that matter, so can entirely synthetic chemicals like lysergic acid diethylamide (LSD). Are they "spiritual?" Our current best scientific understanding holds that the "stuff" we can see and touch (plus most of the things we can't, like radio waves and gamma rays) constitutes around 4% of the known Cosmos. The rest is composed of stuff we call "dark matter" and "dark energy." "Dark matter" apparently responds to and generates gravity similar to normal matter, but it doesn't interact with normal matter or electromagnetic radiation. If it were so that there were enough different, mutually-interacting types of "dark matter" to constitute life, Jim, but not as we know it, would such incorporeal creatures be "spiritual," or "material?"
Once we dispose of the "material/spiritual" dichotomy, which is slippery at best and false at worst, we're back to the two, basic questions that distinguish atheists from theists: Does any sort of deity/deities exist? How would we know?