Of course it would be amazing to know the future (i.e. the whole trajectory of the price process) and it would be really usefull for hedging (it makes the hedging itself a trivial problem). However I think you have to think about that everything in the future depends on stochastic variables and that the only place where hedging makes sense is the present (you always work to be covered right now...at every time!).
In general you can work on the future in a very simple way. Infact at each time $t$ you can just use the initial point $s_t$ instead of $s_0$ in your model.
What changes is that $s_t$ is a stochastic variable rather than a real value like $s_0$. In any case, depending on your model, $s_t$ will depend on $s_0$ (see for example Black Scholes model where $s_t$ depends linearly from $s_0$).
The big problem at this point is that you can not do calibration in $t$ since by definition you need the market data (ok..maybe you can do something with futures value) and this situation stop you from having a proper model for anything.
I hope I was helpful!