Maternity Leave Denied

I live in NYC and work for a large hospitality company. I've only worked for them since May 2019 so I dont qualify for FMLA. I submitted all my leave of absence paperwork to HR and my managers in early January and was never told anything. I'm currently 33 weeks and planned to work until 37 weeks. I reached out to HR to confirm everything was in place and they told me my request is denied until I can provide proof of giving birth!

WTF DO I DO?! Can they force me to work until I give birth since I've been with them less than 12 months? My managers seem perplexed and aren't giving me straight answers on my options.