Greengrocer’s stalls are filled with these custard apples, called ashta in Lebanon and grown locally in coastal areas. Best to buy them still firm and let them ripen at home; their flesh will yield to gentle pressure and the fruit is the sweetest and creamiest you have ever tasted. Maybe that is why they are called ashta here, the Arabic word for cream.
In the US they are grown in some areas (California) and are sold in farmer’s markets; the ones I have bought from supermarkets in the past had been extremely disappointing, so best to get in touch with a grower and buy directly online. They are picked in the Winter.