A pessimistic way of thinking (apologies for my disposition on this entrepreneurial board) is that the odds of being born into an era with the highest population ever to live, are just that: the highest probability.
That we're going to solve the energy crisis, and that this era isn't a brief spike in human population, burning at breakneck speed through the very finite 'windfall' of exploiting found reserves of fossil fuels seems unlikely.
I'm not sure that logic is valid (and thanks to splat for linking a more expanded version of the argument), because the probability of you being born when you were born is now 1. I'm not sure it's valid to try to do logic based on using that as a random variable.
I don't think it's sensible to talk about probability when you only have a single data point and no clue whatsoever of the distribution involved. (E.g. is the human into which you're born actually random as that argument assumes?)
We have mostly solved the energy crisis, in the sense that we have the technical means to supply ourselves with power we can use, and in a sustainable way. Implementing that solution will require rather sweeping political and economic upheaval though, so the question remains for how much longer we'll continue to fuck the Earth's ecosystem before we get around to it (if indeed we ever get around to it at all).
As usual, mankind's biggest problems arise from our inability to scale social interaction well, not from technical prowess (or lack thereof).