The counter argument runs 1) Space is really uncomfortably big. Like seriously, so huge! Also the noise floor is very high and the miniscule radiant intensity of a vessel from size hundred thousand km means that stealth is essentially ubiquitous.
The truth is somewhere in the middle.
The distances involved in space means that you have days to weeks to even months worth of time domain data to use to detect signals that are below the average noise floor. Now combine that time with ever improving computer processing power and no, there is no stealth as popularly envisioned.
Another thing to consider is that unlike NASA telescopes, a military spaceship could cryogenically cool its sensors down to less than the background temperature of space. If we can cool superconducting magnets to less than 2.7 K, then a spaceship could cool its sensors down that low as well. It is simply a matter of carrying sufficient amounts of helium and having enough radiators.
So everything comes down to computer processing power to fulfill digital signal processing requirements.
Outside of its climate science computer, Discover, NASA has less than 12 petaflops to use to sort through data. So if it takes NASA 9 months to find something, then we would need at most 77.76 exaflops to find said object in 1 hour and only 3.24 exaflops to find it in 1 day. The Summit supercomputer ($258 million) weighs 340 tons and runs at 200 petaflops (https://www.olcf.ornl.gov/2018/06/08/summit-by-the-numbers/). Fifteen Summit supercomputers would weigh 5100 tons and should be more than capable of supplying an aircraft carrier size spacecraft with enough signal processing power to see basically everything around it.
Basically, real time detection of low observable objects from long distance in space is an exascale computing problem. Now how big will a future exascale computer be? If past experience is anything to go by, then conventional desktop gaming computers should be at least 1 exaflop within at least the next 20 to 50 years.
But what about quantum computers?
1 quadrillion squared is 1.2676506e30.
A 100 qubit processor would be so ridiculous as to be beyond human conception.
Stealth technology is a bet against the consumer electronics industry.
I'll bet on Intel and friends over military stealth systems in the long haul. I mean, the computer and electronics industry globally outspends the world's militaries on R&D by more than 7 to 1.
And we haven't even touched on sensor fusion. Being stealthy against the entire EM spectrum is laughably hard. Not to mention that most IR stealth schemes rely on a 100 percent efficient means to moving heat to where they want it to go. People unconsciously violate the 2nd law of thermodynamics in these seemingly detailed schemes all of the time without realizing it. Your coolant traveling in a pipe also heats the pipe, which emits IR radiation throughout your ship in directions that you don't want it to go. Even into the reservoir that is your coolant tank to pre-heat your coolant before it goes through your cooling system, thereby gradually increasing the temperature of your craft over time. I mean the hulls in these schemes are insulated, so the IR radiation being emitted by the pipes gets trapped inside of the hull.
The ambient temperature of space in our vicinity is 2.7 K. Physical objects in that vicinity of course will be heated up by the sun, but it will be against a 2.7 K background. So at 36.5 K it will only be 13.5 times hotter than the surrounding space. It is going to be very visible.
Also, your radiating area will not be of uniform temperature. The part in closest contact to the source of the heat, will be much hotter than the parts farther from it.
If your surface has a high reflectivity, then you are by default not stealthy. You have a giant surface that is reflecting over 90% of the incoming radiation. That is a massive signal saying: "here I am, please come shoot me!"
The total power coming from an object = Transmitted (this is the power that it produces) + Reflected (from the sun, active sensor systems, the cosmic background, etc) + Emitted (blackbody radiation). At thermal equilibrium, the total radiation incident on an object producing 0 power = Reflected + Emitted. Any radiation that is not reflected is absorbed and re-emitted as blackbody radiation.
If you line your hull with radar absorbent materials, then you just increased your heat signature, because RAM turns radar energy into heat. So you are more radar stealthy but now you are less thermally stealthy. Line your hull with vantablack, and it will turn incident visible light into heat. Not to mention that it will only be 99.95% efficient at absorbing said light, so you still get a reflected visible light signal in addition to the bigger IR signal (the total is the same as if you reflected 100% of the visible light). Sure, you can move most of that heat around at some inefficiency so that most out of comes out in a different direction or even through the exhaust, but you still just increased the thermal signature of that direction/exhaust. To a distant IR sensor, the ship and its exhaust are just a single point object anyway, which is moving across its field of view and emitting heat above the 2.7 K background.
You are really in a red queen's race when trying to be stealthy in space. If you don't want to get heated up by sunlight, then you need to reflect it, which makes you visible to detection. If you don't want to reflect that sunlight to hide from visible wavelength sensors, then your IR signal goes up as a result of you absorbing the visible light. The same choice is true of radar and UV. The sun emits a lot of energy in the IR band. If you are not IR reflective, then you will absorb that energy and create a higher IR signature anyway.
ag.tennessee.edu/solar/Pages/What%20Is%20Solar%20Energy/Sunlight.aspxSo is your surface going to be reflective or absorptive? If reflective, then you are not stealthy at the frequencies that you are reflecting. If it is absorptive, then you are heating your craft and increasing its heat signature. All of the complicated internal details of how you are going to be stealthy don't really matter. If you are at thermal equilibrium, then all of the power incident on your craft and that you generate has to leave it. When it leaves, then it can be seen. Even if you are cruising around at 3.7 K, you can still be seen. The background is 2.7 K, and a cryogenically cooled sensor (at 2.7 K or below if need be) can pick out that 1 K temperature difference given the long ranges (which mean long travel times and lots of time domain data) involved in space.
In closing, I bet that we have exascale laptops and therefore the computing power to detect stealth spaceships before we have space warships.