Spacecraft configuration

[Aero]

100 to 200 years. That's probably as good a guess as any. I'd just add "years after that first SSTO that can orbit a practical (read heavy) payload." Not so much because of the need for that SSTO, but more for the reason you suggested, the capability for a better payload mass fraction.

[IntLibber]

Edit - Of course there are already perfectly workable SSTO conceptual designs out there, its just that the need doesn't exist.

Just as in 1927 there was no need for a commercial transatlantic passenger plane....