If multiple people each have a first child, are those children collectively referred to as first children or first childs? The former seems more consistent with the usual plural of child, but the latter also seems plausible, since a given person only has a single first child.
A first child is commonly called firstborn; therefore I'd venture to say that the plural form is firstborn children.
The one thing you can bet your paycheck on is the firstborn and second-born in any given family are going to be different," says Dr. Kevin Leman, a psychologist who has studied birth order since 1967 and author of The Birth Order Book: Why You Are the Way You Are (Revell). (...) Psychologists like Leman believe the secret to sibling personality differences lies in birth order -- whether you're a first-, middle-, last-born, or only child -- and how parents treat their child because of it.
However, the same article uses the plural term firstborns. In fact typing the term in Google books receives 36,300 results
Firstborns bask in their parents' presence, which may explain why they sometimes act like mini-adults. Firstborns are diligent and want to be the best at everything they do. They excel at winning the hearts of their elders.
While firstborn children (two words) gets 16,100 hits
Firstborn children really do excel, reveals groundbreaking study
What do Angela Merkel, Hillary Clinton, Christine Lagarde, Oprah Winfrey, Sheryl Sandberg, JK Rowling and Beyoncé have in common? Other than riding high in Forbes list of the world's most powerful women, they are also all firstborn children in their families.
Finally, it can also be written with the hyphen, first-born children. Google Books produces a healthier 390,000 results
Google Ngram suggests that between the mid-1960s and 70s the plural form, firstborns, has taken over firstborn children and is far more common in the US (red) than in the UK (blue), which I confess I found a little surprising.