The Lapis Niger is one of the oldest surviving latin inscriptions, dating to the 6th century BC, and contains a reference to a king. What other historical evidence is there that Rome was actually ruled by kings in its early years, and is there proof that any of the seven legendary kings existed?

Happy to answer this question directly, but I'm traveling for the next few days and won't be able to give it the time it deserves. In the meantime, I've answered a question quite similar in the past - Did the seven kings of Rome before the Republic even exist? If I didn't address something in there that you'd like a specific response to, please let me know and I'll do my best!