There are nomadic people who make cheese even now. I would spend some time looking at what they are doing. A pretty common technique is to slaughter lamb right after it has drunk milk from it's mother. You then carry the stomach all day with you and in the evening, put the stomach in the fire and cut it open to give you cheese.
In terms of aging cheese, in many climates it's absolutely no problem. An extreme example is Chhurpi or Durkha. You don't really need much equipment to make it and it can last for *years*. I don't know what kind of technology we're talking about here, but if you are at the point of pottery, there are some traditional cured cheeses in the middle east that are made in clay pots which are then buried. Another place to look for low technology cheese making is Mongolian traditional cheese made from mare's milk. A lot of that tradition is built on nomadic living and the idea of really being inseparable from the horse that was transporting you. Pre-greek history, the idea of draining cheeses in baskets was already well established as well. Homer writes of it being a technology stolen from the cyclops.
My somewhat uneducated opinion is that it's very likely that the "carry the milk in the stomach of a lamb" trick led *very* quickly to rennet based cheeses and I would venture to say that virtually all early cheeses were rennet based. It doesn't take much experimentation to figure out that you just need to cut out bits of the fourth stomach and add it to some milk that's been sitting in the sun for a few hours to make pretty awesome curds. They will be wondering why the milk in a lamb's stomach forms solid curds, while milk in a hide bag just makes yogurt. Then it's just an exhaustive search of what body part is making the magical cheese. From there, draining it in a reed basket is trivial. Roman documents show that hard cheeses were aged in the shade and I've got to imagine that this piece of knowledge is as old as agriculture.
I'm kind of rambling here, but the key thing to realise is that the moisture level of rennet cheeses is determined almost solely by how early and how small you "cut" the curds after the form. So any impatient person who pours the forming cheese out of their hide bag into their reed basket a bit early will find that they get a dry cheese that ages well. The other important thing is that curds knit with absolutely no effort *at all* at a high pH. So this theoretical impatient person will not only get a dry cheese, but also a cheese that forms into a very nice compact cheese. From my perspective, I'd be shocked if it even took a single generation to go from draining cheese in reed baskets to aging them for as long as they want. Find a low humidity place to dry the cheeses and you can make something that will shatter your teeth if you want to.
