Welcome! I saw your post in the hybrid section, and was going to suggest that you ask here as well, and it looks like you've already found the place to be!

When you say that your bike has a "sealed cartridge" bottom bracket, I take that to mean "square taper" (which is commonly called "sealed cartridge"). If you Google "shimano un55", does that resemble what's on your bike (not necessarily the color, but the style, with the square tapered ends)? If so, then you'll need a new square taper crankset, with three chainrings. SRAM's website doesn't seem to indicate that the S-1000 crankset comes with a square taper option, but it's possible, especially for an OEM (which is why I ask that you confirm the bottom bracket type).

You'll need a new left side shifter, one that supports three chainrings. The M6000 series shifters ARE available with 3-speed left shifters, so you should be able to find a left side shifter that will support the change (SL-M6000-L).

Is your front derailer also a Shimano Deore M6000 series? It looks from Shimano's M6000 series website that they have versions optimized for 2-speed and versions optimized for 3-speed. You will likely find best performance from one of the 3-speed versions. They have different mounting styles to accommodate different frame designs. Personally, I'd probably see if I could get your bike set up using extant 2-speed derailer and see how it goes. You may find that you'll want to change it out, but you also may not. That'd be a bridge you might not have to cross.

Your rear drivetrain (derailer and cassette), and chain, will be compatible with a crankset swap. Good luck!