While the provided search results were not helpful, the quest to find a majestic Silver Lynel is a worthy one for any seasoned adventurer. Hunting these creatures is the ultimate test of skill, and I can certainly guide you to their lairs.
The most important thing to understand is that Silver Lynels don't just appear from the start. They are part of the game's hidden scaling system, meaning they will only begin to spawn in the world after you have defeated a significant number of other enemies. If you're only finding red or blue ones, keep fighting and getting stronger; the silver variants will eventually take their place.
Once your world has leveled up sufficiently, one of the most reliable places to find them is in the Depths. A key location is the Floating Coliseum, found directly beneath the Coliseum Ruins on the surface. Here, you will face a gauntlet of five Lynels in a row, and as you progress, the final one will be a mighty Silver Lynel, with the others eventually becoming silver as well.
On the surface of Hyrule, you can often find them in the same remote clearings where their weaker counterparts once roamed. Check the Nautelle Wetlands in Lanayru or the Kamah Plateau in the Faron grasslands. Another common hunting ground is in the northern Tabantha Tundra. Head to these locations after you've conquered many other foes, and you will find the challenge you seek.
