I don't think the siblings or the date of the parents' marriage were put in birth records
That's not how it works. You'll first need to find the birth record of your ancestor, which also names his or her parents. Once you have the date of birth, you go backward in time to look for the marriage of the parents. If your ancestor was the oldest child, the marriage is usually found the same year or a year earlier. If the ancestor is not the first child, you'll have to dig backwards through the records until you find the parent's wedding.