It certainly can be bootstrapped by PoW, but doesn't need to be (and usually isn't in practice). The initial stake if it's not bootstrapped by a different consensus mechanism is simply created (not too differently than PoW creates coins). You have an initial block that anyone can create (but in practice, it's generally the creators of the coin who do that), and then the coin created in that and subsequent blocks is distributed in some way (sale, give aways, etc). The fairness of the distribution is always something highly scrutinized by the larger cryptocurrency community, and many coins (pow and pos) have massively unfair distributions of their currency (ie to themselves as a money making or "funding" scheme).
> Does 'proof-of-stake' need to be 'bootstrapped' by a period of 'proof-of-work'?
I think it's optimal if they do, because proof-of-work is more fair in the beginning, so it's easier to do a fair distribution launch with PoW. With Proof-of-stake, I've never seen a network launch that didn't result in a cartel.
PoW algos adjust difficulty based on how much hash power is in the network. So you could do this, but people would see it and react to the demand plus you'd also have to sell most of the mined coin in order to cover your electricity costs.
Does 'proof-of-stake' need to be 'bootstrapped' by a period of 'proof-of-work'?
If the 'work' part is very simple and requires little effort, then couldn't I generate a 'stake' that's just as large as someone else's very easily?