Despite the hopes of many retail investors, SpaceX will probably not have an initial public offering (IPO) anytime soon. Unfortunately, this fact means small investors cannot buy or sell shares on a stock exchange.
Most small investors cannot buy SpaceX shares; instead, institutional and high-net-worth individuals can buy shares. However, it is still possible to own a piece of SpaceX either directly or indirectly.
Probably the most straightforward and least risky way to gain exposure to SpaceX stock is by buying Alphabet (GOOG, GOOGL) stock. In 2015, Google invested $900 million with Fidelity Investments in SpaceX.