Could it be insects? Do the leaves show any signs of damage or distress?

There is no visible insect damage and the plant looks very healthy except last year it heavily rust damage on all the leaves. Here is another photo showing the fruit starts to develop bruises on its skin As it grows.

There is no rust damage as of now

Right off the bat I'd say the plant looks healthy. If the fruit hasn't been damaged in any way, it could be the plant indicating its not able to support it. The plant looks kind of young and doesn't really have an abundance of leaves especially right there where all those figs are. I've seen them produce fruit in that condition, but this one just may not feel it can do so. How has your weather been? If its been as cool there as it has here that may be a cause for dropping the brebas to focus on the main crop. What variety is it? Green figs often get blotchy as they ripen. Have you cut one open to see if they are edible? Wish I could advise you better, but that plant will most likely get it together soon.