Not hazelnuts, but I do it with sunflower seeds all the time. The way I do it is just to soak the seeds overnight, drain and rinse, blend with water and the contents of a probiotic capsule until pretty smooth, then keep in a warm place for 18-24 hours. Usually the last few hours aren't all that warm cause the stove has gone out overnight or something. With the probiotic capsules I find that a longer, cooler ferment tastes better anyway.
It does thicken, but it's more like buttermilk than yoghurt in thickness. I'm just using an immersion blender or my Oster beehive, and the mixture stays a bit grainy. If you want creamy, you'd need a high speed blender, I think. Even then, i don't think it'll be creamy like dairy. The solids might separate out, leaving a kinda nasty looking dark "whey" at the bottom of the jar. Maybe hazelnuts don't oxidize like sun seeds, though. I just give the jar a shake before using. I'm eating it, not displaying it 😁
I wouldn't say the flavour is amazing. I don't eat it on its own, but it's good in porridge. Hazelnuts might taste way better, though. They don't have the bitterness that sun seeds have. And you can always blend in some dates and vanilla extract or cocoa, nutmeg, etc. once it's cultured. I do that occasionally with fresh sunflower milk (pulp strained out) for green smoothies, and it's quite nice that way.