Tubers Cave appears to have come out in February 2022. A YouTube upload titled “21st Of February 2022 Roblox Tubers Cave Gameplay” strongly suggests that date, and another source ties the Tubers93 “Fave”/Tubers Cave event to early 2022 as well.

Quick context

  • The Tubers93/“Tubers Cave” Roblox stuff was part of the broader Tubers93 hacking saga.
  • Most references place that specific cave-related game/event in February 2022.
  • There isn’t a single widely agreed “official release date” visible from the sources I found, so February 21, 2022 is the best match for the named gameplay upload.

TL;DR

Tubers Cave came out in February 2022, likely around February 21, 2022.