According to Daren Dochterman (who worked on Star Trek Voyager as well as the Director's Cut of Star Trek the Motion Picture), the original Star Trek titles were hand drawn by Richard Edlund who worked at the Anderson Company (the company that did the special effects for the original series).
Final Frontier is NOT the font used in the Original Series. It is a font that is based off the logo for the first Star Trek Motion Picture. Therefore, it did not exist prior to 1979, and certainly not in the mid-1960s when the Original Series aired.
There are a wide variety of clones and fonts inspired by the Original Series Star Trek font. But the hand-drawn nature of the logo is apparent upon close examination. Simply compare the two Rs in the Star Trek logo. They are not identical. The left one (in the word STAR) is wider than the right one (in the word TREK). It is also important to notice that the characters used in the episode title cards also varied from the six unique characters in the Star Trek logo. Most specifically the E character's upper left corner is rounded in the the main credits (in the "Star Trek" title and also "William Shatner" & "Leonard Nimoy" credits) but not in the rest of the production credits (or even in the "DeForest Kelley" credit). So while the production crew must have created a font for use in the credits, it didn't exactly match the "Star Trek" logo's characters.
Linotype sells a font named "Horizon" that is clearly inspired by the Original Series logo & credits font, but it has characters that are clearly different. It is one of the few Trek-inspired fonts that has the correct V character, but the B and to some extent K & Y characters do not match exactly. And none of them have the E character with the single rounded corner.