Genetic testing

I went in for my first prenatal appointment a couple of weeks ago and when going over things with the nurse she asked me if I wanted the genetic testing done. She explained that with my and my husbands medical history and family history there shouldn’t be any concerns and that the test would be purely optional and therefore probably not covered by insurance. I decided not to have it done if the nurse felt there was no reason to be concerned. (My husband was not allowed in the appointment due to Covid so I had to make the choice on my own on the spot) My husband is concerned that this means we will have no idea if our baby has any health issues until its born, but I’m under the impression that many tests are done throughout the pregnancy to check for any abnormalities. Should I be concerned? This is my first pregnancy and I really have no idea how all of this works. My husband is very concerned that there will be something wrong with the baby, but I’ve been very relaxed so far, and I’m 13 weeks today. I haven’t had any bad feelings or gut feelings that something is wrong. Other than I get occasionally worried when I have a random sticky CM, but it’s not consistent. I guess I don’t know what to expect or what tests will be done in the future.