The world of video games is packaged with male lead characters, but pinpointing the exact moment a female protagonist was introduced is more challenging than you might think – especially when you take into account arcade and home releases and the global nature of the video game market.
Game historian Kate Willaert has posted a fascinating thread on Blue Sky which tries to chart developments, admitting that the topic "isn't as cut-and-dried as folks might like to think."
Willaert notes that Exidy's 1977 title Score (a reskinned version of the highly controversial Death Race, released in 1976) is the first arcade game where you could select a female character; the aim was to choose either a man or a woman and then chase the opposite sex around the screen.
Three years later, Teknon's Tropical Dive appears to have introduced the first female playable character for Japanese audiences, although this isn't clear as no original machines exist and the game has not been dumped and preserved; as Willaert says, many Japanese companies simply used attractive women in promotional material and not in the game itself (interestingly, Score is also a "lost" game).
If that is the case (and it's hard to see the main sprite in the fuzzy screenshots that exist for Tropical Dive), then Japan's first female protagonist will almost certainly have been found in an arcade game called Streaker by Shoei, released in 1981.
To confuse matters further, Willaert explains that between the years of 1977 and 1979, four computer games were released which allowed you to choose whether your character was referred to as male or female – but these did not show your character on-screen. These games were Oubliette (1977), Avatar (1979), Santa Paravia en Fiumaccio (1978), and MUD1 (1978).
If we're talking about the first designer-created female protagonist (rather than a nameless, optional gender choice), then Willaert cites Tawala's Last Redoubt from 1981. Published by Broderbund (which would later release the popular Carmen Sandiego series), its main character is a woman called Benthi, but she doesn't appear on-screen at any point during the game.
We'd highly recommend you dig into Willaert's thread, as the answer to this question is more nuanced than you might expect.