I love tracing the origins of little fandom things, and the question of when 'sueyuu' first popped up in anime/web serials is a fun one because it digs into how voice acting became a thing in Japan. If by 'sueyuu' you mean '
seiyuu'—the Japanese voice actor profession—then their roots go way further back than most casual viewers realize. Japanese voice acting evolved out of radio drama and stage acting in the early 20th century, and when animation moved from experimental shorts to full-length films and television in the 1950s and 1960s, those same performers started providing voices. So, technically, actors doing anime voices have been around since the earliest days of mainstream anime—think the era around films like 'Hakujaden' (1958) and the breakthrough TV series 'Astro Boy' (1963), which used trained actors rather than anonymous narration.
What made seiyuu distinct as a recognizable, dedicated profession — and not just actors doing a side gig — happened gradually across the 1960s to 1980s. As anime moved onto TV and series production ramped up, certain performers became associated with the industry, and agencies began specializing in representing voice actors. The 1970s and 1980s saw the rise of iconic names who were identified with particular character types, and by the late 1980s and 1990s the phenomenon of seiyuu as media personalities really took off: they started appearing on radio shows, releasing character songs, and performing at concerts. I still get nostalgic for the era when cassette singles and drama CDs were how we fangirls and fanboys got more of our favorite characters’ voices — it made seiyuu feel like proper stars.
When it comes to web serials and internet-native works, the timeline shifts later. The internet allowed independent creators to cast and credit voice actors for online audio dramas, Flash animations, and later web animation projects in the late 1990s and 2000s. Fans started producing amateur dubs and web serials with volunteer voice talent even earlier, but professionally cast voice work tied specifically to web-origin stories really became feasible as broadband spread and platforms matured in the 2000s and 2010s. Around that time, established seiyuu began appearing in web-based projects and virtual performances as well, especially as streaming and social media let talent connect directly with fans.
So, in short: voices in anime go back to the earliest mainstream works in the 1950s–60s, and the seiyuu profession as a distinct, celebrated career crystallized through the 1970s–90s. Web serials and internet-first projects started bringing in credited voice actors in earnest in the 2000s onward, with a mix of professional seiyuu and passionate amateurs. As someone who collects old drama CDs and watches both vintage anime and new web series, I love seeing how a craft that began in radio drama has blossomed into such a diverse, internet-friendly culture — it feels like a living timeline you can hear in every character performance.