Ever since the Meiji era, at least. Prior to the accession of Emperor Meiji to the Chrystanthemum Throne, court diviners changed the era based on fortuitous or inauspicious natural or astrological events.
They're a held-over tradition from back before the Europeans arrived, bringing the Western calendar with them. Telling someone when a certain event happened would be pretty much like "the XX year of YY".
Taishō was pretty short (1912-1926), but there should be a few. The Tenryū class, for example; they were both constructed starting in 1917, so they're comfortably within that era.
(Partly, it depends on how you reckon it. For example, all four Kongō-class ships were laid down during the Meiji era, just barely, and Kongō herself was launched just a few days before it ended, but none was commissioned in that era. On the other end, the Fubuki class was a Taishō-era project, and the first couple of ships were laid down in that era, but no ship of that class was launched, much less commissioned, until Shōwa.)
Taishō was pretty short (1912-1926), but there should be a few. The Tenryū class, for example; they were both constructed starting in 1917, so they're comfortably within that era.
(Partly, it depends on how you reckon it. For example, all four Kongō-class ships were laid down during the Meiji era, just barely, and Kongō herself was launched just a few days before it ended, but none was commissioned in that era. On the other end, the Fubuki class was a Taishō-era project, and the first couple of ships were laid down in that era, but no ship of that class was launched, much less commissioned, until Shōwa.)
Most of the older battleships (Yamashiro - Mutsu) are Taishou. Fuso was laid down in the Meiji era, as were all the Kongos. Houshou is fully Taishou, and Akagi and Kaga are partly Taishou, commissioning afterwards. Furutaka-class is fully Taishou, while Aoba-class is mostly Taishou. Myoko-class was laid down in the Taishou era, but launched afterwards. Tenryuu - Sendai-class cruisers are all comfortably Taishou era. Including Yuubari. Kamikaze-class and most of the Mutsuki-class are comfortably Taishou era. All the Mutsuki were laid down in that era (barely for Yuuzuki), ten were launched in that era, and seven were commissioned in that era. Five of the Fubuki were laid down in that era. Mamiya is Taishou era. Kamoi is Taishou as well.
For non-Japanese ships: Gangut was laid down and launched in the Meiji era, but commissioned in the Taishou era. HMS Warspite is a Taishou era ship. HMS Nelson was laid down and launched in the Taishou era, but commissioned afterwards. Aquila (as SS Roma) was Taishou era ship. USS Saratoga was laid down and launched in the Taishou era, but was commissioned afterwards.
Gotland of course was always there. (shh she wasn't)
Even Meiji and Shōwa shipgirls will be in the same boat!
We are all HAAAAAAAAAGS, wot!!
(Modern) Eras go Meiji → Taishō → Shōwa → Heisei → Reiwa. Heisei is the current one (when this image is posted), with Reiwa starting on May 1, 2019, at which point all KC shipgirls' can be considered 'born' at least two eras ago (hence hags/grannies).
