Here's what the indexes themselves say:
"The S&P 500ยฎ is widely regarded as the best single gauge of large-cap U.S. equities. The index includes 500 leading companies and covers approximately 80% of available market capitalization."
"A globally recognized index of 100 of the most innovative large cap companies listed on the Nasdaq Stock Marketยฎ."
"Represents 100% of the US investable equity market"
You're telling me that you don't think SpaceX post IPO fits any of those definitions?