I looked it up and unsurprisingly there's a whole Wikipedia page about this. Long story short, it takes decades for rock to become soily at all so likely a much longer time till it becomes as soily as what's around it here.

In Iceland it’s pretty cold a lot of the year - not insanely, but colder than a lot of plants prefer. So the rock to soil conversion happens via moss.

While on tour there last year, our guide pointed out the ages of certain lava fields, and he noted that the existing lava fields around Grindavik were between 700 and 1300 years old. My photos from the area show that they’re about 60-70% rock, with moss covering the rest. I suspect if you scraped away the moss, you’ll find slightly crumbly rock underneath (But don’t do that - do not mess with the moss in iceland). I’m not sure how long it takes for the lava to be converted into soil, but I would guess it’s more on the scale of multiple thousands of years.

This page (up until the waterfall) has some good photos of a few lava fields and gives dates for the eruptions that created them. Meandering Wild - Lava and Moss
(The photos are at the bottom of each blurb, not the top - so Eldhraun is the one with the rounded rocks and moss at 350 years old, and not the black rocks, and Dimmuborgir, at 2300 years old, is the one with the treetops shown below the craggy rocks.)

Another banger from our tour guide was that (according to him) the locals say if you get lost in an Icelandic forest, just stand up. Which is… sorta true. They only tree of real quantity there is birch, and the tallest birch I saw was about 16ish feet (5ish meters). They do not grow heavily, so they’re a bit comedic and stringy. Decades old stands of them sort of look like 1-2 year old stands planted in warmer climates - without any ground cover, of course, because while grass will grow, the usual complement of weeds, vines, and what-not does not.