Star Fox - Corneria

Zelda Ocarina of Time - Deku Tree

Contra 3 - The Streets of Neo City

Donkey Kong Country - Jungle Hijinx

Donkey Kong Country Tropical Freeze - Mangrove Cove

Metroid Prime - Frigate Orpheon

Final Fantasy VI - Narshe Mines

Final Fantasy VII - Mako Reactor 1

Golden Eye 007 - Dam

Turok 2 - The Port of Adia

Zelda Breath of the Wild - Great Plateau

Sonic - Green Hill Zone

Limgrave is absolutely stunning, but it's so massive that it's hard to classify it as an opening level. You can take as long as 15 hours to beat everything, it even features a huge legacy dungeon

Oh yes, great choice, this might actually be it. The game as a whole is too uneven to really be great, but that first level is phenomenal. There are some other really good ones late in the game, but none that tops the opening level.

A bit similar to Sonic 1, which also suffers from uneven level design, but Green Hill Zone is definitely great.

Another game that has a great first level, but fails to keep the high quality throughout I think is Halo 4.

Then there are some games, that are just great throughout, but also happen to start on a high note - Doom (1993), helped a lot by the killer soundtrack, The Elder Scrolls IV: Oblivion, if it counts, has pretty great opening, it is a tutorial, that is a solid dungeon in its own right, with some storytelling in there, it is just long enough to get you used to the basics, without dragging in the least. Super Mario 64 has a great first level, that delivers on the sand box style gameplay from the get go. The Last of Us has a very strong prologue.

The openings for any of the first three God of War games are perfection, imo.

To add to what's been posted already, Uncharted 2 throwing you right into an awesome setpiece with the falling train set the tone beautifully.

Sonic Adventure 2 - City Escape

Breath of the Wild - Great Plateau

Persona 5/Royal - Bank Heist

Super Mario Galaxy - Good Egg Galaxy

Xenoblade Chronicles - Battle of Sword Valley

Yeah this is one of mine too, just masterful in the way it teaches the player about the game's mechanics through level design.

1-1 in Super Mario Bros does the same thing, serving as an intuitive tutorial where you learn by playing.

Metroid Prime's opening with the frigate Orpheon is also masterful in its ominous tone and commitment to immersion, and I'd also give a nod to RE4's village fight and Bayonetta 2's city sequence for starting their games off with an epic bang that only gets better.

God of War seems a bit famous for its high action setpiece openings:
God of War 1: Hydra on the ships
God of War 2: Colossus of Rhodes
God of War 3: Posseidon on Olymp
God of War Assencion: Giant monster corpse moved by other monster (forgot the names)
God of War 2018: Troll and Stranger fight
God of War Ragnaök: Björn and Thor

The first one that comes to mind is the escape from the Pillar of Autumn in Halo: Combat Evolved. “Escape intact as Covenant forces board your ship.” It’s daring, and tense, and sets the stage, in both mechanical and narrative terms, for the adventure ahead of you.