job search - How to finish PhD and get through the academic job market as a new mother and primary caregiver?

I am a female graduate student in a competitive phd program. I recently had a baby. Although this is a planned pregnancy, and I thought I had thought through the complications having a baby would bring, I am still very overwhelmed by how much different my life is now.

I don't have any time besides taking care of a newborn, and I am very sleep-deprived. Baby's dad works full-time to support the family. Even though it brings me a lot of joy, I just can't help but wonder whether I would ever have time for my research again. I initially planned to go back to school in September, when baby will be about 3 months old. But I am not sure whether I would be able to do anything next semester. Or even the semester after next. I initially planned to graduate next fall, but now I feel that might be a stretch. The application starts next semester, and I should be going around giving talks and preparing for my applications. But that feels impossible now.

And there is the financial stress. I want to put my child in daycare at some point (like around 7,8 months), so I can have some time to do work. But it's very expensive, and I don't know if we can afford this with our current income. Sometimes I thought about finding an industry job after graduate school, so things would be easier. But I don't want to give up research.

What is an effective way to deal with the stresses of being a new mother while on the job market? Specifically, how can I complete my research and apply to jobs in a situation where I am sleep deprived and child care is expensive?

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This is a different question than Having children while at graduate school because I believe a female student's experience is different than a male student's experience. Especially at infant stage, mother's role cannot be placed by others due to constant feedings. The author in the other post also has his girlfriend/wife staying at home with the baby, so there will be much less work for him. In my case, I would be the one taking care of the baby since my husband works full-time. Another thing is I am already at the stage that I am about to graduate as opposed to the other post is debating whether to start the program, so I am more concerned about the graduation timeline.