Preheat your oven to 425°F (220°C) and line a large baking sheet with parchment or aluminum foil. The goal is to have a single pan that fits everything without crowding.
Toss the cubed sweet potatoes with 1 tablespoon of olive oil, half the minced garlic, paprika, thyme, salt, and pepper. Spread them in a single layer on the baking sheet. Give them a head start since they take longer to cook than salmon.
Roast the sweet potatoes for about 12 minutes, until they start to soften and caramelize a touch at the edges.
While the potatoes roast, pat the salmon dry with paper towels. Brush or drizzle with the remaining tablespoon of olive oil, lemon juice, a pinch of salt, and pepper. If you like a garlicky kick, rub a little minced garlic on the fillets.
Add broccoli to the sheet, tossing it with a quick drizzle of olive oil, garlic, and a pinch more salt and pepper. Make sure the broccoli is spread in a single layer so it roasts rather than steams.
Nestle the salmon fillets among the potatoes and broccoli on the sheet pan. If you have lemon slices, tuck a few around the pan for a bright finish.
Return the pan to the oven and bake for 10-12 minutes more, until the salmon is opaque and flakes easily, the broccoli is tender-crisp, and the sweet potatoes are fork-tender. If you prefer your salmon well done, give it a couple more minutes—but watch it closely to avoid overcooking.
Remove from the oven and let everything rest for a couple minutes. A final squeeze of lemon over the salmon wakes up the flavors. Serve hot, with a quick pinch of flaky salt if you like.