What an odd question – I'd love to know the story behind it. But anyway, I'll take a stab at it.
First, some definitions. The Stone Age is a very long time period starting when our ancestors first started using stone tools 2.4 million years ago and ending with the first use of metal tools which, depending on which part of the world you're talking about, was anywhere between 7,000 and 50 years ago. For simplicity let's say it ended somewhere around 5,000 BCE. Garlic bread is toasted bread with garlic butter on it.
So, I'm a Stone Age chef looking to make garlic bread. Let's go through the ingredients one by one and see if I can find them:
Bread, i.e. ground cereals made into a dough and baked, has been the staple food of much of the Old World since people first started farming in Southwest Asia 10,000 years ago. But it was also made less frequently from wild cereals much earlier than that; currently the earliest evidence comes from 30,000 years ago, but probably it goes back even further. No problems here.
For butter the first thing I need is milk. Unless I'm willing to use breastmilk, this will have to wait until at least 10,000 years ago when the first milking animals (sheep and goat, then a bit later cattle) were domesticated in Southwest Asia. But making butter from milk is quite an involved process, will people have bothered? As it happens, we know that people must have been processing milk (into cheese or butter) from the beginning, because the gene that allows adults to digest lactose did not become widespread until several thousand years after we know people were milking animals, and therefore raw milk was inedible. There is direct evidence that people processed milk into something from 9,000 years ago, and widespread evidence for cheese-making from 8,000 years ago. So depending on where I live I might not be able to get hold of "butter" as we know it (i.e. churned, pasteurised cows' cream), but I could probably find some sort of processed milk product, be it something like ghee or a soft goats cheese, that would do the job.
Wild garlic is native to Central and Southwest Asia, and so would have always been available to people living there. We don't know exactly when it was domesticated and spread, but there is early evidence of it being used in Southwest Asia 4,000 years ago.
As for cooking technology: all I need is a grinding stone to grind cereals for dough, a fire to bake and toast the bread, and something to mash up garlic with butter. All readily available at any time in the last few million years. Pottery, which came into use 16,000–8,000 years ago, would probably be useful for churning the butter and mixing in the garlic but conceivably an animal skin or gourd or something could be used instead.
So if I lived somewhere in Western Eurasia in the latter part of the Stone Age, after 10,000 years or so ago, yes I could probably make garlic bread. We have no idea whether anyone actually did.