In all probability, the sound occurs just as often at other times but you don't hear or at least notice it with the daytime background noise, moving around in the house, etc. Also, one effect in many animals, including humans, is when asleep (or about to go to sleep) your nervous system puts more emphasis on hearing - both because the other senses are not receiving sensory input, but also as a hereditary defensive mechanism to wake you up if you hear noises when asleep. So - you tend to notice or react to a lot of noises at night that you would ignore in the daytime.
Here is a recent response on pipe creaking - which could well be what you are hearing, though you did say not related to water running so less likely.
Other alternatives - heating system exhaust duct expansion and contraction related to either the furnace/boiler or the hot water heater heating, housing on one of those creaking as it heats and cools, forced air furnace ductwork creaking as it expands and contracts - those should be easy to confirm or rule out, by listening near them as they fire and then cool down. If noise does not last long enough for you to run ndown there when you hear it, to force firing if you don't want to wait around for a long time have someone turn up thermostat (to turn on furnace/boiler) or run hot water (to make hot water heater fire).
Ditto if you have an on-demand water heater that might be cooling off and creaking as it cools down due to no use/
Also, on rare occasions, water softeners will make this type of noise during their flushing and self-cleaning cycle, especially with plastic tank ones - check what time of day yours is set for, and maybe make in daytime instead.
I have also heard this creaking and popping against wood quite loudly in older houses with a large (30-60 gallon) expansion tank mounted in the joist space overhead near the boiler/hot water heater - look like this (second photo)-
Also if you have a large overhead expansion tank likethat be sure it is not filling with water, because its weight could be causing joist creaking or it might be pulling connections free if it is - should be mostly full of air.
Otherwise, try running water (usually hot) and see if that makes it happen - then follow suggestions in the first link above about tracking whether it is water or drain pipes - in my experience, more commonly plastic drain pipes if a hard, sharp knock and metal water pipes if a creaking or ratcheting type noise, but more types of pipes can make several variations of noise.
Since you say wakes you from sleep, obviously if no one has gone to the bathroom or run water in the few minutes before that, takes that out of play.
If you have baseboard (hot water) or steam heat, those systems very commonly cause this sort of noise. The creaking or ratcheting click is more common with the pipes, condensed water in radiators can cause a very sharp bang - like someone hit the floor or radiator with a hammer.
I suppose it is possible there is a structural problem, but normally creaking and cracking of joists or trusses splitting or breaking come in just one or two noises at a time, not spread out over 30 seconds or so - and fairly quickly if this is going on day to day you would be noticing deflection of the floor or basement ceiling; or cracking of foundation walls if due to a foundation problem like from expansive soils or a sinkhole - quite rare for houses to have that problem, but can cause this sort of on-going audible noise. You could contact your building department about whether expansive soils or sinkholes are common in your area.
I don't suppose it sounds like clicking of nails - and uyou have a critter settling down to sleep or getting up to go to the bathroom in the night and you are hearing that (assuming this is more of less right below your bed). Or a squirrel getting up for a midnight walnut snack and you are hearing teeth cracking seeds/nuts - or chewing on piping.
Best bet if just listening around with your ear against faucet,walls, etc - I would buy a $10-15 METAL (plastic ones not as goodfor this) stethoscope at a box store pharmacy area and keep by bed, then next time you hear it just up and see if you can track down the source by listening at pipes, ducts, walls, floor, etc before it stops. Might take you several times to track down the exact location, narrowing down the search area each time it occurs until the sound stops.
Then when you tie it down you will know what sort of repair is needed - if duct might be a joint that needs joint sealer and some pop rivets, if duct or pipe creeping against wood then a protective plastic collar or rubber pad may be needed, or the opening around the duct/pipe opened up a bit. If creaking housing on water heater/furnace sometimes a few more sheet metal screws (or tightening) will do it - I have seen a couple of cases where it just could not be stopped until a brick or two was put on top to weight it down so it could not move. Had one old standup oil-fired boiler whose outer casing creaked terribly - like a halloween horror movie special effect - ended up putting a couple of bands of polyester shipping strapping around the housing to quiet it.
If in the flooring and you can't tie it down and does not seem to be flooring expanding and creaking because it lacks perimeter expansion room, then you might have to open up an inspection hole in the basement ceiling - head size hole, or about 1/2" hole and use illuminated fiber optic camera to look up in there and see what you can see, and maybe to use a rod or piece of wood to push against pipes or ducts while noise is going on to see which is making the noise.
One other thought - if you have a setback on the thermostat at night, try temporarily setting the night temp the same as daytime and see if that stops it - might if the creaking is from ductwork shrinking during the cooler night conditions.
Also - I presume this couldnot be something loose or hanging by the house, and you have been having wind gusts at night. Our snow shovels and such hanging by the front entry do this at time - bang a few times to half a minutes or so, just once or twice a night on breezy nights when the angle of the wind is just right. Try checking round outside and unhang anything that could be banging against the house.