The singular form of "дівчата" is "дівчина", and it is feminine. However, there is a colloquial word for "a girl" with the same root - "дівча", and it is neuter!
But you're right, "дівчата" does look like a plural of a neuter word. It could well be that etymologically "дівчата" was formed as the plural of "дівча", but I can't be sure. Just treat it as an irregular plural for now.
You are right here in the sense that дівчата comes from дівча -> дівчато (?) -> дівчатко which is neuter. But it is also plural for дівчина which is feminine. And in this case it follows the same declension patterns as the plural of neuter words (e.g. кошенята). Sorry, didn't quite understand what you wanted at first ^^
I'll just mention in passing that words for young people are often neuter e.g. German Mädchen. In Slavic languages, the ancient root "dit-" gives neuter nouns like Russian дитя (now archaic, but with plural дети, the usual modern word for "children").
I wouldn't say that дівчата (being plural) has no gender. Perhaps the gender is not visible in Ukrainian, but some Slavic languages distinguish gender in the plural. For example, in Serbian "The men left" would be Мушкарци су отишли but "The women left" would be Жене су отишле.