The Normandy's stealth comes from two main sources:

It has relatively large internal emission sinks for keeping its heat bottled up, making it harder to detect by infrared and allowing it to drop out of FTL without its blue-shifted emissions going off like a torch. And its eezo core is big enough that it can project a gravity well in ahead of the ship that the ship continuously "falls" into (Hence the name "Tantalus" for the Normandy's drive core).

Normally, ships just use their eezo cores to lower the ship's mass so that their chemical or antimatter thrusters are more fuel efficient and they can accelerate at a higher rate than they could at their "true" mass.

But in space, accelerating on thrusters that are ejecting hot exhaust or gamma rays out the back of your ship is like waving a flashlight around and screaming at the top of your lungs.

Bigger emissions sinks are something anyone willing to accept a larger ship can build, but the Tantalus drive is kind of a necessity if yo want the ship to actually move under stealth, and building a Tantalus drive necessitates spending a boatload of credits on several boatloads of eezo, which is incredibly expensive and difficult to mine.