How can I make hazelnut essence, or some strongly hazelnut-flavoured liquid, without using sugar or alcohol?

I would say you are out of luck, unless your requirements are less strict than they appear to me.

There are three main solvents in cooking: water, alcohol (*), and fat. You cannot use alcohol, so we are left with water or fat.

Hazelnuts contain lots of oil and little water. So it is possible to press hazelnut oil, therefore there is no need to try to make an infusion. This is about the strongest you can get. When I buy hazelnut oil, it tastes as if made from raw hazelnuts, not roasted, although it should be possible to make it with roasted ones. In any case, you are left with a liquid which has an unmistakeable hazelnut taste when eaten pure.

However, it would be highly unlikely that somebody tries to eat hazelnut oil in ways where it can be tasted pure, except maybe to dip pieces of bread in it or to pour it over a salad. If you try mixing it, you have two problems. First, it is an oil, and won't mix with anything that is water-based. Second, the aroma is not as concentrated nor as volatile as in a hazelnut liqueur. I don't know how you want to use your liquid, but if you want to add it to stuff (cakes, ice cream, whatever) as an aroma, you will have to use a large amount to get a very small hint of hazelnut.

With water, the best you can make is hazelnut milk, since it is not just an infusion, but also contains some of the original hazelnut solids suspended in the milk. Again, it is strong enough when tasted on its own, but cannot be added spoonwise to something else to achieve hazelnut taste - it will have to be the main ingredient somewhere. So you can use a recipe where the base is mostly water and replace it with the hazelnut milk, but not, say, bake a cake and hope for strong hazelnut taste.

Concentrating a water based concoction may be possible to some extent, but you are more likely to end up with the equivalent of double-strength coffee, not the equivalent of nescafe, when using procedures accessible to the home cook.

Other solvents exist, but they are not foodsafe in the amounts required for making infusions at home. Industrial processors use them when they have some synthetic aroma which is way too strong, to dilute it into usable levels.

So, to sum it up, you cannot make something at home which, when used in small amounts, can flavor a large batch of food, the way you can do with, say, vanilla essence. But if hazelnut oil or hazelnut milk are good enough for you, then you can easily get hold of those, or even make them at home if you invest in the proper equipment.

^{* In this post, I use "alcohol" to mean "ethanol", because this is the standard meaning in cooking and everyday life. If you mean "alcohol" in the chemical sense, please edit it into your question, since this is not obvious when you simply use the word "alcohol".}