The pawpaw, Asimina triloba, seeds I received from JLHudson were a no brainer to plant. I’ve grown quite a few pawpaw, and the really critical things are to keep the seeds moist until planting, make sure they go through a cool period before you expect them to sprout, and protect the young seedlings from sunburn.
The JLHudson catalog describes the seed as perishable (it is!) and that it has been stored moist and refrigerated, which is the only acceptable way to store this seed. That means that it is ready right now to go into soil and probably sprout above the soil in about 2-3 months. That would be late in the year for most fruit trees, but should be just fine for pawpaws.
I picked some of my deepest available pots for this. The tap root is very large compared to the above soil portion of the plant. The seedlings really do need shielded from UV light when young. And the trees do not tolerate being dug up and moved around. All these things add up to starting them in deep pots so they can be grown in the greenhouse (or under shade cloth if need be), to be planted in their permanent location after 2-3 seasons of growth in pots.
Keep them watered!