Really, the most implied answer is that, if the gods didn't exist, there wouldn't be anything anyway because they created everything, so there would be no mortals to use magic.
Design proposal 3: Withdrawal of Emptiness (magic)
The ritual of Withdrawal of Emptiness employs the powers of order and chaos to manipulate space, smoothly moving a target object from one place to another by withdrawing space from between those places and moving it to the other side. Because space is warped continuously, nothing occupying the path of transit experiences any effects - it's more like pushing the threads of a weave aside to open a hole than like cutting them. The distance travelled and the size of the object are both harshly limited by the ability of the mage - complex projects would probably require many mages working together.
Design proposal 4: Thaumatomotor (infrastructure)
The thaumatomotor is a simple construction of overlapping layers of metals with varied elemental attunements, arranged so that part of the device, called the rotor, spins relative to the remainder (the stator) when arcane force is applied. Because it runs on raw arcane energy, only the most basic magical understanding is required to operate the thaumatomotor, and only a modest amount of mental effort actually has to be expended to run it, so it can be much more efficient than developing specific spells for some particular use. It can, obviously, be used to power a wide variety of systems throughout our domain, from smithies and mills to wells and vehicles.