How can I make cookies without any sugar?

No, there are no other agents. Caramelization is literally sugar in a certain state. If you remove all the sugar, you cannot have a caramelization taste. You can make cookies which don't taste caramelized, of course.

As for the "important structurally" part, it depends what cookie you are trying to make. If you want to achieve the texture of a sugar-rich cookie, this is again impossible. Out of all edible substances, only sugars behave like sugars when baked.

You can however use other fillers to get a different type of cookie. A shortbread cookie (like pie crust, but in cookie form) with stevia shouldn't taste that much different than a shortbread cookie with sugar. Nut flours or nut butters will give you some very good fillers so you can make a cookie with some bulk without having to use too much flour.

The result will never look and taste like a standard American chocolate chip cookie, or its relatives but will certainly deserve the term "cookie".

It likely depends on what you qualify as 'sugar'.

America's Test Kitchen, in their recipes for gluten-free flour replacement suggested using powdered milk to enhance the browning. As that would contain lactose (a sugar), that might not fit within your requirements.

My husband cannot stand the taste of stevia in anything, so I've been having similar problems. I've been told by my doctor to cut down on sugar (easier said than done for my sweet tooth). I have substituted Monk Fruit sweetener and it does work well, but it doesn't seem to be as sweet as sugar. I have found, with certain recipes, that a combination of Monk Fruit sweetener and pureed pitted dates works well when the recipe calls for both white sugar and brown sugar. I just change out the white sugar with Monk Fruit and the brown sugar with pureed dates, same measurements. I've used this in cobblers and cookies. I hope this helps.