As noted in other replies, the ARPANET predates IP and TCP. Although some Internet applications, like Telnet and FTP, were first implemented on the ARPANET, I don't consider it to be the Internet in any meaningful way. The Internet was conceived as a network of networks, which directly affected the design of TCP/IP. Thus, the Internet proper began with the transition to IP. ARPANET was a test bed, to see if packet switched networking would actually work. It did. So well, in fact, that the ARPANET was used for actual work, until it became obvious that something better was needed to replace it. That replacement is the modern Internet.

I enjoyed this book about the development of the ARPANET: https://www.amazon.com/Where-Wizards-Stay-Up-Late/dp/0684832...