Sooner than If sentence structure [closed]

The "if" clause is basically the protasis of a third conditional. It is used to describe a past situation that did not actually occur, and it requires the past tense of "to have" along with a past participle (in this case, "had matured"). The UNC Writing Center describes this construction as follows:

This conditional deals with situations in the past that are unreal—they didn’t happen. We can still imagine what the consequences would have been. . . . When the situation is unreal and in the past, use past perfect (had + -ed) in the conditional clause and would have + verb in the main clause.

In case you're wondering what happened to the apodosis, it has been omitted. We could include it thus:

After a female dolphin loses her calf, she can give birth again much sooner than she would have if her calf had matured to adulthood.