I believe I have a black mulberry tree in San Diego CA but all the mulberries seem to die they seem to start growing but the die.
The tree is green and looks healthy.
This is common when there is too much nitrogen in the soil. It can also happen naturally, as they produce way more fruit than they can support. They will drop most of this pretty early on.
If it continues, and you never get a single fruit, then I would apply fertilizers high in phosphorous and potassium, but very low or no nitrogen. This will help it to retain fruit, and cut out some of the nitrogen. This article will help you with the care of these trees: https://www.gardeningknowhow.com/ornamental/trees/fruitless-mulberry/how-to-grow-mulberry-trees.htm