I have a feeling you might be mixing some things up. Just to clear, there are two separate programs but they interact with one another.
DCFMLA is like job insurance. It means that if you have a baby, your job will still be there for you after you take some leave. This is an old program that has existed for a few years already. The type of leave does not matter, as you can take paid leave, unpaid leave, short term disability, etc. but that is totally up to you. It allows you to stay away from work up to 16 weeks for medical and 16 weeks for family during a 24 month period. So for instance you could do 8 weeks medical and then 16 weeks family and then still have your job (or something "similar" to your job) available when you get back. This program is better than federal FMLA. Since it is better than the FMLA program, this program supersedes federal FMLA and you get the benefit of the better program. These are the eligibility requirements for DCFMLA:
* Employed by the employer for at least one year without a break in service
* Worked at least 1,000 hours during the 12 month period immediately preceding the requested leave
DC Paid Family Leave (DCPFL) says that you can take paid leave after pregnancy that will get you a percentage of your wage back. The most you will get are 8 weeks of paid leave. I think this is what you are referring to. The eligibility requirements are a bit more complicated so you might want to ask HR. The important questions are:
* Are you mainly based in DC (over 50% of your work time is there)?
* Does your employer pay unemployment insurance to DC? If so, they are most likely paying the employer tax that pays for DCPFL.
* Or simply ask whether you would be eligible for DCPFL.
July 1, 2020 is called the effective date. This is the date when DC can start paying out claims for paid leave. My understanding from what I've been reading is that it is not a cut-off, so your May birth is fine. What still needs to be determined is whether you can put in your paperwork before this date. If you can, then you can start getting paid for family leave on this date. If they don't start paperwork until this date, you won't be able to take your paid leave until after they process your paperwork.
So just to give you an example in your situation (using made up numbers since I don't know your leave balances). You could take 2 weeks of sick leave, 3 weeks of vacation, and then 8 weeks of DCPFL. That means you have used 2+3+8 = 13 weeks of paid leave. According to DCFMLA you can now take 11 weeks of unpaid leave (or paid leave if you can find a funding source) and expect to have your job when you get back.
Much of what I said is based on what they posted on the DCPFL website. They haven't officially posted guidance yet, so you might need to wait a few months to get a true answer to your question.
References:
DC FMLA -
https://ohr.dc.gov/sites/default/files/dc/sites/ohr/publication/attachments/DCFMLA_Poster_March2016.pdf
DC PFL -
https://dcpaidfamilyleave.dc.gov/resources/
Edit: Changed months to weeks. Thanks for pointing that out!