Countering or masking steady background noise in apartment

Just moved into a new building. The steady HVAC sounds from the building are rather loud in my bedrooms. (I guess HVAC is what generates the noise, it never shuts off or changes but I’m not sure what else could be the source, other ideas are welcomed.) As the noise is very constant (similar to what some websites list as green or blue noise), is there a way to counter the noise with another noise? Or do I just have to mask it with a louder noise that I prefer? Thanks.

Noise-cancelling headphones or earbuds would probably work very well to attenuate a constant steady hum. But you may not want to wear them all the time. Other than that, I don’t think there’s any way to mitigate the noise other than mask it with a louder noise.

Is it coming through the air vents or the walls? If it’s the air vents, then maybe a few baffles in the vents or over them can mitigate it a bit.

You do need to work out what the source is. Depending upon what it is some mitigation may be possible.

One point about noise is that in a room the reflections matter a great deal. Dampening the reflections can make the apparent noise level drop.
Curtains, soft furnishings, carpet, rugs, wall hangings can help.

HVAC noises can be addressed with treatments in ducting. Or to a lesser degree on the exit of ducting.

Noise can leak in from the outside through the tiniest of openings.

The ideal is to get the builder owner to abate at the source. In the meanwhile the same noise canceling techniques used for headphones are available for speakers, specific to this sort of usage.

https://www.silentium.com/home-appliances/

How about adding sound-deadening acoustic tiles to your walls if the building owner can’t or won’t do anything to ameliorate the noise? It doesn’t seem too terribly expensive, unless you have a lot of wall surface to cover.

https://www.amazon.com/sound-deadening-materials-walls/s?k=sound+deadening+materials+for+walls

Also you could use noise canceling speakers using them to play an ambient nose app with a sound profile that you prefer. The noise canceling aspect would give it a competitive edge over the objectionable sound.

I’d suspect red or brown noise would work best to offset the high frequency blue to green noise.