Wow, that's an interesting question. I would think that as soon as the lava has cooled enough for someone to build on it the island would be habitable by people. This could be only a few years or less. For other life to live on it, like moss and grass, flowers and wild animals a soil layer would probably have to form first. This could take many decades.

Short answer: not long at all! The big island of Hawaii is still a volcano, and is still growing, and people actually live on it. In fact, whole towns have been wiped out by sudden changes in lava flow. The big island of Hawaii is unique as far as volcanic islands go, however. There are parts of the island that are 4 million years old and other parts that are less than a day old. This is why people can live on it even though it is still being formed. If the whole island were covered by cooled lava (solid rock), then there would be no soil for plants to grow, which would mean that whoever lived there would have to import all their food. Recently formed lava is very porous (has lots of holes formed by bubbles trapped in the lava as it cools), and so rainwater tends to flow right through lava, rather than remaining on the surface. This would make it hard to find a large supply of drinking water on a recently-formed island. Soil and older lava rock (in which minerals have plugged up the holes) is much better at trapping water. So the long answer to your question is that the length of time it would take for a volcanic island to become habitable is the time it would take for the rock to weather and form soil and for plants and animals to colonize the island. Weathering processes (rainfall, temperature changes) and certain plants (lichen) play an important part in soil formation by helping to erode the rock, making it weaker and more likely to break it into smaller pieces. But this is only the first step in soil formation. Lichens and certain bacteria are also important because they increase the fertility of new soils by making nitrogen more available to plants. (Nitrogen is required for plant growth.) Plant seeds would have to be carried to the island somehow (for Hawaii, wind and water probably brought the initial seeds). Because of the harsh conditions (no shade, little nitrogen, coarse soil), the first types of plants to survive would be weeds, which are usually not edible. However, palm trees can also tolerate rocky, sandy soils, and their seeds are carried long distances by water. Palm trees would help provide building materials and food. Plants that produce fruits have flowers and so require pollinators. Although some plants are pollinated by wind, it is likely that a few insects and bird species would be necessary to get a variety of fruits for eating. However, once the insects and birds arrive, they can carry seeds from nearby islands and help increase the diversity of plant life. Where do you think humans living on this island might find protein?