To be honest the only way that you can reliably speed up your cycling process is to take
Mature Media from another filter and place it in your own.
Water / Gravel will contain very little effective bacteria to make much difference.
Its the Filter Media that contains the high concentrations of bacteria that you require to
run your tank without showing ammonia spikes.
I've just set up a breeding tank by replacing a 1/3 of the media in the new filter with old
media from my community tank. This was after running the new filter for 2 weeks in the community tank.
48 hours later I have had no ammonia spikes and perfect water stats.
I really don't think old water or old gravel substrate would make enough difference on cycling times.