* The *Star Trek* franchise? If so, it began in 1966 with the original *Star Trek* series.
* The *Star Trek* brand? This is less clear-cut. While *Star Trek* has been a popular brand for decades, its official branding has evolved over time. It's hard to pin down a single date when the brand was "created".
It's important to be specific when talking about "Brand - Star Trek" as it could mean different things depending on what you're asking about.