It is truly magical how every single new product Apple releases goes out of stock very shortly after going on sale, creating a frenzy for people who want to be lucky enough to acquire one - only to be followed by adequate stock being available very shortly thereafter.
But one thing we can be certain of - this is NOT a marketing ploy by Apple to inflate demand.
/s
It isn't a marketing ploy, it is called physics. I'm going to introduce you to a few concepts that you might not be familiar with so see if you can follow along. Making new products takes "time". You don't just place an order for millions of complicated devices and get them constructed over a weekend. Also you can only start making the new product after you have fully designed and tested the prototypes. So "time" before completing the design and testing can't be used for making the product.
When a new product is introduced, customers have not yet acquired it. So there is this thing called "demand", which in the case of Apple often peaks right at the introduction because it is at that point that the highest number of customers who do not have the product exist. As the product is delivered to customers, demand is satisfied. So demand decreases as the products are delivered.
Also, while the product is being delivered Apple gets more "time". Apple uses this time to make new products.
Eventually equilibrium is reached as demand starts matching the time Apple has to have more of the product made.
The only way for Apple to have on hand enough product to satisfy the initial surge of demand is to hold off on announcing and selling the product. Apple could then get more time. Apple could have made iPad Minis for two months and secretly stockpiled them (with many invariably slipping out). But that would have just allowed Amazon, Google, and Microsoft more time to play in the mini tablet space without an Apple competitor. That would have been a terrible strategic decision.
There are only so many factories in China with so many workers that are capable of making these machines and all the various components. You also can't, at this point, just increase the number of factories devoted to a product for a couple of weeks. Configuring a factory (and training employees) to make a product like this takes time and money. The factory needs to stay devoted to the same product for a significant period of time to spread those costs out in an economic fashion.