Perhaps not entirely Earth-like, but depending on the technology available in your universe/race/story, you could do something similar to an idea taken from The Life of Pi.
Pi Martel encounters a floating, carnivorous algae island, large enough and stable enough to host a colony of Meerkats, as well as himself and a full-grown Bengal tiger. With a little bit of research, we find that this isn't too far-fetched, as stories of natural floating islands DO exist. Here's two notable examples: Cranberry Bog, Keibul Lamjao National Park. There are also explanations of large masses of peat rising from the bottom of swampy areas, stable and thick enough to support shrubs and trees.
So depending on the properties of the plant life on your world, combined with some technology and minimum (if needed) handwavium, a terrestrial ecosystem could be naturally established, or established through man-made means in a semi-natural way.
Edit for explanations:
Without more detail on the flora of the planet, here are a few general ideas of how it could be achieved.
A. Masses of entangled plants could be detached from the seabed. Depending on their composition and entanglement pattern, they may need some buoyancy help, or none at all. The rigidity of the floating mass would also help shape architecture of any humanoid life on the planet.
B. Plant life suited for colder environments that has certain features causing it to be buoyant and stable could be brought in from other ecosystems and stimulated in the new environment. Ideally the plants would be able to form some sort of symbiotic relationship with some of the local fauna.
C. Reaching a little more far-fetched here, a species of plant that is known to have rather massive growth could be planted in areas of the ocean where said species of plant will be capable of breaching the surface and fanning out. That species of plant would either need to be capable of growing underwater, or would have to be planted in a specialized man-made environment until it was fully matured. The specialized environment could either be built on-site, and removed once the plant matured, or could be built off-site, and transported and transplanted.
D. Branching out (haha. sorry.) from plants towards my most far-fetched idea is floating sponge islands. To maintain the buoyancy, the humanoid race that I assume is going to be living there could run a system of pipes through the sponge, drawing water out of the sponge layer and eject it back into the ocean. Since I don't know much about your planet's location relevant to any nearby star or it's atmosphere, I'm going to assume it's cold due to lack of sunlight, so you'll have to reconcile the obvious power costs of such a system somehow.
Hope these help!