Job interview at 38 weeks!

Al

So I do not currently have a job, I graduated with my BA last month and I need a full time job in September after baby is here! I applied for an insurance company and have a phone interview on Monday! But baby is being evicted the Monday after! Do I tell them in the interview that I am having a baby and will need time to recover? Or just tell them I wouldn't be able to start right away? What would you do?