Bring a medium pot of salted water to a boil and cook the linguine according to package instructions until al dente. Reserve 2 tablespoons of the pasta water before draining.
Pat the salmon fillet completely dry with paper towels and season both sides with half of the sea salt and black pepper.
Heat the olive oil in a non-stick skillet over medium-high heat. Once shimmering, place the salmon skin-side down in the pan.
Sear the salmon for 4-5 minutes without moving it to ensure the skin becomes crispy and golden. Flip carefully and cook for another 2-3 minutes until the center is just opaque.
Remove the salmon from the pan and set it aside on a plate to rest. Reduce the skillet heat to medium.
Add the minced garlic to the remaining oil in the skillet and sauté for 60 seconds until fragrant but not browned.
Stir in the cooked linguine, reserved pasta water, lemon juice, lemon zest, and fresh baby spinach. Toss continuously until the spinach is wilted and the pasta is glossy.
Transfer the pasta to a plate, place the salmon fillet on top, and garnish with parmesan cheese and the remaining salt and pepper.