Almost nothing survives from Earth's original skin — the Hadean proto-crust was swallowed back into the mantle. The first continents that stuck show up in the Archean as a distinctive suite of pale rocks geologists abbreviate TTG (tonalite–trondhjemite–granodiorite) — grey gneisses that make up roughly two-thirds of Earth's most ancient crust.
They formed by partially melting wet, basaltic crust deep down. Whether that happened at early subduction zones or by other means — mantle plumes, great gravitational overturns of the crust — is still genuinely debated. What's not in doubt is the product: thick, silica-rich, low-density rock. These buoyant masses are the cratons, the ancient, stable hearts at the core of every modern continent. Because they're lighter than the ocean crust around them, they float high and resist being dragged back down — which is precisely why they've endured for billions of years.
The TTG continents appeared in bulk between roughly 3.8 and 3.5 Ga, and by about 3.3–3.2 Ga the first of them had grown thick enough to rise clear of the sea. Dry land had arrived — and this time, to stay.