Yeah, this is super common and almost always harmless. The weird taste and black specks are just loose carbon dust from the manufacturing process. It's not dangerous, but you shouldn't drink it.
The fix is simple: you need to flush the filter. Run cold tap water through the new filter for a solid 15 seconds before you even put it in the pitcher. After you install it, you still need to discard the first three full pitchers of water it makes (or use that water for plants). That should clear out all the carbon dust and any other initial taste.
IF THAT DIDN'T WORK: If the taste persists beyond the first three pitchers, double-check that you pushed the filter in firmly so the groove lines up with the ridge in the reservoir. A bad seal can cause issues. Also, never use hot water—the max is 85°F (29°C). Hot water can damage the filter and cause off-tastes.
HEADS UP: Remember, this filter isn't a purifier. Don't use it with water that isn't microbiologically safe to begin with.