I would treat them like blueberry seeds because they are in the same family.
I successfully germinated many hundreds of blueberry seeds by taking a few of the best and biggest blueberries from my deepfreeze, thawing them in water and letting them go mushy, then spreading them over potting mix (or soil raisin mix) in punnets in a greenhouse. The freezer experience will duplicate waiting through a cold winter and trick the seeds into germinating when they are on warm soil.
The tiny seedlings came up thickly and I waited until the first true leaves appeared before very carefully transplanting to individual small pots with the help of a fine bamboo skewer. Keep moist and don't let them dry out at any stage. You should use acidic potting mix (for azaleas) if you can get it. Feed occasionally with weak organic liquid fertilizer. It may take a couple of years before the plants are big enough to plant out.
Persimmons grow from fresh seed immediately potted up - just wait.
Good luck and let us know how you get on.