How was God able to produce clothes for people during Adam and Eve's time?

It is well known that the earliest humans made simple clothes out of animal skins.

It's a good thing Edison invented a light bulb, because it gave them someone to screw into the light sockets that were wired to switches. Sometimes inventions (of clothes, for example) came about due to necessity.

The Prophet Adam and his wife Eve, peace & blessings of God be upon him, always had clothing in the Paradise when they were in Paradise and when they ate from the forbidden tree, they lost their clothes of paradise. God is our true Provider, He gives us everything we need and that includes clothing. 

They figured it out. Early man was quite intelligent, contrary to the teachings of the religion of evolutionism.

I have a few musings on your question. To begin, when someone believes in a god, they tend to believe in that god as being omnipotent (all powerful) and omniscient (all knowing). Based on this, I think it is assumed that if God wanted to make clothes, we'd say it's not only well within his power, but it would actually be so easy for him (as making clothes is a skill that even us human folk can grasp) that the task itself, even for millions living at the time, would be seen as almost trivial to an all powerful being such as himself.
Secondly, I don't think it's believed that God ever made clothes because I'm sure that in the Bible, Adam and Eve only feel the need to wear clothes after they leave Eden. This I believe is because after eating from the tree of knowledge, they gain knowledge of all things, including shame - which makes them choose to start covering themselves up in embarassment. Because of this, I don't think God did make them clothes in canon, but rather that Adam and Eve learnt to be resourceful and to make use of their environment when cast out by God, and so in turn made clothes for themselves. This knowledge would have been passed down through their descendants meaning that God, like usual, would never have to intervene in the clothes-making process.As for now, clothes are still definitely made by people, not God, and usually in mass production by big factories all over the world that sew and stitch them together. They probably still use similar techniques to make clothes as humans always have, and it's just style that changes with time, but sadly, still no divine interference.I hope that helps to answer your questions - I'm no expert, but I've tried my best! :P

Hand Me Downs from some other failed creation 

Chapter and verse, where does it say they eore clothes?

First of all, Adam and Eve didn't exist. So, anyone who thinks they have an answer is making it up.

I would think that during the process of evolution, humans at one point learned to make clothing from hides or cloth to keep themselves warm, just as they discovered fire, the wheel, weapons and tools to help them in everyday life. Now doesn't that more sense? 

When God made them, "man and woman, he made them from 
the dirt of the Earth" they probably did not need clothing. But when God made the second woman from the rib of Adam, she demanded a wardrobe. It is hard to imagine how God pulled it off, but suffice it to say that if he can make a universe, creating clothing was not a problem. 

Don't know why you think Moses' day was a problem, but God fashioned leather clothing for Adam and Eve. Meaning he either killed an animal, being the first person to shed blood, or created it from nothing, which makes having to kill animals for their skin seem pretty pointless and cruel.

People knew how to make clothes during Moses time.  Don't be stupid.