You might find it most efficient to break the simulation into
two pieces since simulations always start from "now" (t=0).
The "history" could be one simulation and the history-
based result, a second.
In the break, you could (say) cause a result to be printed,
manipulate that result into an initialization-of-variable
file, and then have your "now to future" segment read
that as part of its setup.
Of course that's a dance that is difficult to get through the
GUI, and you might end up needing Ocean scripting for
Cadence, or SPICE / shell scripting in some combo for
other platforms.
I used to have to do this a lot when I was working on laser
trimmed analog parts. Became -much- more difficult when
Cadence dropped cdsSpice (great yet simple filesystem
access) for Spectre ("Command language? What's a command
language? We don't need no steenkin' command language!
Oh, all right, here's Ocean, you whiney bastards, enjoy the
suck").