Where is the grease on my front brake caliper coming from?
Assuming you have hydraulic disc brakes, the most obvious explanation is that you have a brake fluid leak in the front caliper. If the grease isn't appearing anywhere else it must be coming from the caliper itself. Shimano uses mineral oil as hydraulic fluid which will feel greasy, the black color is road dirt sticking to the oil. 

You can probably prove this by thoroughly cleaning the rotor, pads and caliper (inside and out) with degreaser, reassembling and applying the brake hard several times. Remove wheel and pads and look for fluid in the caliper (the pads are already contaminated so this won't do any further harm). DON'T try this with the rotor and pads removed as you will over-extend the pistons and they may come out of the caliper body, resulting in all your fluid spilling on the floor. Alternatively you can use a bleed block in the caliper to retain the pistons.

If the bike was bought new the store you bought it from should fix or replace the caliper for free.