Pretty simple question. Whether you're launching a spy satellite, building a top secret orbital missile weapon, or investigating a mysterious alien artifact in orbit around Earth heralding the return of the Starborn ones, could a large satellite remain hidden from modern humans long enough to do anything interesting with it (from a narrative perspective at least) or has our information-gathering technology become too sophisticated to hide from?
Space debris is well-tracked by both public space agencies (NASA, ESA, presumably the Russians and Chinese too), and military and intelligence organizations (such as....haha you thought I was going to tell you?).
Here is the reference on Wikipedia. According to this bulletin, there are over 17,000 distinct things in orbit being tracked by NASA. Here is a paper about the capabilities of the Space Based Visible satellite.
In general, any object over 10cm in LEO to Geostationary orbit is being tracked. Keep in mind, those are cold specks of debris. There is extensive IR monitoring of space by military and intelligence groups, to determine maneuvering capabilities of potentially hostile satellites. If a satellite was energized and operating, it would be radiating heat which would certainly be detectable by multiple modern nations at least out to the moon, maybe further. It might be harder to detect satellites over the poles; I'm not sure where each countries monitoring stations are, but the US/UK/Canada/Australia joint sites certainly have 100% global coverage.
Hide in plain sight.
Call it a weather satellite, or a communications satellite, or something boring and mundane like that. Actually include some of that hardware so that it can pretend to play the part. Launch it with two other satellites and a six-pack of cubesats as part of a standard commercial launch. And then, oops, a "malfunction" after launch causes it to wind up in an "unexpected" orbit. Some sort of navigational or computer error. Announce that, not to worry, it's in a safe orbit. And since you don't want to lose your investment, you're going to keep monitoring it to try and nudge it into a useful orbit.
Now you have a satellite up in whatever orbit you actually want, that everyone dismisses as "that lost satellite", and if someone notices that it's maneuvering, well, no big deal, its all just part of the painstaking satellite recovery process.
Although stealth technology doesn't work in space (according to the first comment on your question), you might be able to piggyback on an existing satellite or previously-identified piece of space junk. That is, you could bring your new satellite (through handwavium) close enough to an existing satellite to dock with it. That would create a single blip on radar screens. So long as your satellite didn't interfere with the operations of the existing satellite, it may go undetected.
Plus, as Truman said in the movie Armageddon, "[We can] track about 3% of the sky, and begging your pardon sir, but it's a big-ass sky."
You would also need to launch your satellite into orbit as a secret component of another, legitimate launch.
A lot depends on how far an orbit you accept. This is especially significant because its an asymmetric situation - a satellite very far from earth becomes harder to detect, but might only be little affected by the extra distance, or the physical size needed to allow good angular resolution.
Example - imagine a spy satellite used to video some specific part of earths surface (a military zone for example). Space-based optics are routinely able to be extremely high quality because there is neither distortion from gravity nor from atmosphere. Think Hubble telescope in an orbit some millions of miles from earth, photographing periodically when the orbit is favourable. Harder to detect.