In some ways, a sign language seems more intuitive than a spoken one. Vision is generally more communicative than hearing, and signs could be made to resemble what they refer to. Chimpanzees and gorillas have also been taught to sign. It doesn't seem terribly likely that sign language would come first, but lots of unlikely things have happened.
Spoken language is a pretty early development. You may want to ask /r/askanthropology about that one, as it would likely pre-date any recorded history.
There's a great book on this possibility.
The Gestural Origin of Language
This book uses evidence from and about sign languages to explore the origins of language as we know it today. According to the model presented in this book, it is sign, not spoken languages, that is the original mode of human communication. The book demonstrates that modern language is derived from practical actions and gestures that were increasingly recognized as having the potential to represent and hence to communicate. In other words, the fundamental ability that allows us to use language is our ability to use pictures of icons, rather than linguistic symbols. Evidence from the human fossil record supports the book's claim by showing that we were anatomically able to produce gestures and signs before we were able to speak fluently. Although speech evolved later as a secondary linguistic communication device that eventually replaced sign language as the primary mode of communication, speech has never entirely replaced signs and gestures.
Plus there's Deaf communities where sign languages spontaneously appeared over a few generations, such as Al-Sayyid Bedouin Sign Language and also bilingual bimodal hearing and Deaf communities, such as Martha's Vineyard.
signs could be made to resemble what they refer to.
This is called "Iconity" and is a very interesting topic!
You could also ask /r/linguistics too.