No. Because you do not yet have an eligible child. I am assuming this upcoming birth will be your first.
Now you used the word "enroll". While you may "enroll" now, just make sure contributions to the account don't start until "AFTER" the baby is born.
Some things to consider too. (..and it pains me to say this.) What if something happens between now and then such as a miscarriage? That would create a tax problem for you that you don't need at such a time as dealing with the grief
What are the requirements for having a dependent care FSA? First, your employer must offer one. You also can’t use money from a health FSA or a limited health FSA for child care expenses. You or your spouse must work or be looking for work for the child care costs to be eligible. You and your spouse may contribute up $5,300 if filing jointly. If you’re filing single or married filing separately, the limit is still $2,650 – like a normal FSA.
For the dependent care costs to be eligible, the child must be under 13 years old. If the child turns 13 during the plan year, any child care expenses after the birthday are ineligible. But: If you have a child or other dependent relative over age 13 who is mentally or physically incapable of caring for themselves, your dependent care FSA can be used to pay for expenses.