Bitcoin unfortunately began with an immediate expansion period:
From every conceivable angle, I cannot see why it wouldn't have been better to distribute the coins via an s-curve, with block rewards maximizing at a certain point after launch.
The exact time it should take before block rewards maximize is up for debate, but I believe this approach allows time for everyone to learn about your project and get involved without feeling like they have "missed the boat". It also allows your network to fail early and often before the majority of the coins have been generated.
Please explain from a game theory standpoint why this distribution is not superior in every way to one that begins immediately at the expansion phase? (with the exception that ultra early adopters don't get as rich).
If you are worried about the network not being taken seriously because miners won't waste their time on a currency whose future block reward is greater than the current one, do some thought experiments with an infancy growth phase of 1 to 3 months and ask yourself what would happen. Sure... perhaps an infancy phase of years might not work, but I believe that letting the buzz build for a few months at a minimum is a superior way to launch a new cryptocurrency.