Shinto was not really an organized religion in the early era of Japanese history, but rather part of a diverse world view. The problem of course is untangling what Tokugawa-period nativist intellectuals said about Shinto; what modern Japanese ideologues said about Shinto as the source of Japanese unity and uniqueness; and the details of the reinvention of Shinto after the Pacific war from what is actually born out in the historical evidence.

There are early texts that some would claim show the prominent influence of Shinto on early Japan, like the Kojiki and Nihon shoki, but these texts also point to the enormous influence of people and ideas from China. So do they show the influence of "Shinto" on early Japanese culture? I'm not sure they do.

We see some clear connections such as the importance of mirrors both in these early texts, in later Shinto practice, and in early archaeological excavations.

Also important is the myth of Amaterasu, the sun goddess, who is enshrined at Ise and who is a major figure in the texts mentioned above.

Lastly, certain court rituals emerged in the early period--as early as the reign of Emperor Tenmu in the 7th century--that show a divergence from Chinese and Korean practices. Perhaps those represent the beginning of Shinto in a kind of institutional form?

Michael Como's 2009 book Weaving and Binding is a great scholarly source on many of these issues. You might also consult this online resource for the study of Shinto from Kokugakuin University in Japan: https://www2.kokugakuin.ac.jp/e-shinto/