Nervous about pumping for daycare

I'm nervous about having to pump. Everytime I do at the moment I make maybe an ounce to an ounce and a half in between feedings. If I feel engorged I'll make like 2oz on one breast. I'm currently almost 6weeks pp. My son eat about 2.5oz every 2-2and a half hours. And I'm so nervous I won't be able to pump enough milk for him. I'm not sure if my milk comes in more over time (I hope) but I'm worried I won't be able to breastfeed for long. What have yall noticed over time with your supply? Does it come in more over time?