Some related questions on ScienceLine cover much of this question. Essentially, the hard, nutrient-poor top layer of rock which forms immediately after an eruption must be transformed into an environment suitable for sustaining life. First, the area has to cool down enough that plants won't simply burn.
In Hawaii, volcanologists have found that this can take weeks, depending on the thickness of the lava flow and the weather (for example, rain will speed cooling). The initial rocky layer must then be broken up for several reasons, such as to allow water to be retained instead of running off the top, and to form crevices that collect dirt into which plants can sink roots. In addition, the chemical composition of the early soil, which might be highly acidic and unfriendly to plant life, must be returned to a more hospitable state.
Some of the minerals in volcanic ash and rock can make for very fertile soil, but they need to be brought to the surface and harmful elements removed. Further, even if the environment is able to sustain plant life, the seeds need to be transported to the volcano, land in appropriate soil, and experience the right conditions to germinate.
There is no common timeline for these restoration processes; every volcano and every eruption is different, and the recovery depends on multiple factors. The climate of the region is one of the most important though. Stronger wind, rain, and large temperature changes will hasten the weathering and erosion* processes which convert the inhospitable surface into one amenable for life.
A few examples from the above linked webpages: on Krakatoa, a few plants (mosses and lichens) were found 3 years after eruption, and grass was found after 11 years; at Mauna Loa, 75% of an eruption site was covered in moss and lichen after 5 years, and trees were present at another after almost 50 years. Meanwhile, Mount St. Helens had flowers just 1 month after essentially destroying the surrounding 200 square miles of forest. The timing of the eruption, the surrounding plant life, and the weather/environmental conditions helped Mount St. Helens to recover faster than many expected, but it seems that, eventually, nearly all volcanoes will host life.
* Subtle difference - weathering is in place while erosion involves transport between places.
First I will say that while the volcanic eruption will kills plants and animals in the immediate time, the resulting soil is quite rich in nutrients, so plants will eventually grow back just as lush (likely more lush) than before. So now to answer “how long is eventually.” This largely depends on the location- particularly how much rain is received. Let’s take Hawaii as an example- an area that receives a lot of rain was reported to have ferns and small trees growing about 2 years after lava flows. A nearby spot on the drier side of the islands has spots with flows over 100 years old with barely any growth. Since you asked specifically about grass- I would say rather quickly- grass comes in many varieties and is rather fast growing- so no matter where the eruption/lava flow was, I bet there would be some form of grass that would at least start growing a bit within 2 years.
It can be as quickly as ~1 year, but more often much longer than that - sometimes even decades or longer. In order to grow plants, you need to make soil, which forms when rocks break down. You also need seeds to be planted in that soil. How fast a rock turns into soil depends mainly on two processes: how much rainfall that area gets (think the rainforest vs the Mojave desert), and the type of rock. Some volcanoes, like those in Hawaii, erupt lava that breaks down very easily. Other volcanoes, like Mt. Lassen (a volcano in CA that erupted in 1915), erupt lava that doesn't break down as easily. So in that case, you would get soil to form first on the Hawaiian lava flow, because it turns into soil easier than lava from Mt. Lassen.
Other factors are where the volcano deposit is at. If it's near a vegetated area (like a forest), it will be easier for seeds to come from other grasses/trees and land on the new soil than if it was farther away from a forest. And the type of stuff that comes out of the volcano matters, too. If ash falls on an area, it will be easier for plants to come back than if a lava flow were to come through and completely cover the ground, making new land (so the plants have to start all the way over again).
Please see the ScienceLine answer from 2016 here. How soon plants regrow after an eruption is highly variable and depends on how completely they were covered, what type of lava or ash they were covered with, and how much rain or snow falls afterwards. Some grass-like plants have started growing back within six months, though it usually takes longer for them to get well established.
Before grass or other plants with stems and leaves can grow, there needs to be some sort of soil, which generally forms as lava rocks and ash break down and algae grow on them. The algae and later lichens also decompose and form new soil that grass can grow in.
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