Strange Minecraft Noise
Solution 1:
The sound you heard was very likely one of the intermittent ambient sounds that play when you're in a dark area (the linked site lets you play each sound so you can check to see if one of the sounds is the same one you heard). It might be a little unsettling but they're harmless noises. If you're hearing them inside your new base it's an indicator that you haven't lit it up enough and you have some areas that are dark enough for mobs to spawn.
It also could be an Enderman screech, which is the sound that plays whenever something aggros an Enderman.