If by Stone age you mean an era lasting 4 million years, no, that didn't exist.

If by Stone age you mean an era unbroken between 3000 and 2000 BC, no, that span was broken by the Flood.

If by Iron age, you mean the very first use of iron was after the Bronze age, no, that's inaccurate, Tubal Cain made iron before the Flood.

However, there is a correct usage, and it mostly refers to the post-Flood world.

Probably some tools were on the ark, in metal. But very probably these soon became inadequate to those on board. And after the Flood, they were not finding metal ore any time soon. This is the main beginning of the stone age.

However, this was not the first stone age. Before Tubal Cain, stone tools had been used, and some populations, like the Neanderthals we found, held on to that technology up to the Flood. Someone of Neanderthal lineage was on the Ark, and could instruct the others in stone tool making.

The Lower Palaeolithic, and part of the Upper Palaeolithic (as long as you find purebred Neanderthals) is pre-Flood, regionally stone age, while the contemporary Nodian civilisation was so far not found. But the rest of the Upper Palaeolithic is the 350 years after the Flood when Noah was still alive. Then came the Neolithic, with Nimrod in Göbekli Tepe, as his original Babel is now called. Abraham was born when the Chalcolithic was still ongoing and saw the birth of the Bronze Age, which was still ongoing in Joshua's time./HGL