Something to note about Beet J Stag's canon is that it is tied into the Greater United Toei Multiverse. Due to a series of crossover movies and events, the loose timeline follows and applies to several canons across the board in DDD:
1974: The Riders were born, and sometime during this time, they were destroyed. As a result, Riders began to be born across the Rider Multiverse. This world was then known as The World Without Riders.
1974: During this time, Super Sentai were born, and throughout the generations, at least once a year a new team was born to fight the evils. This became the foundation for what is known as the World Without Riders, aka Super Sentai World.
1974 to 2004: Numerous other heroes were born as well, Zubat, Inazuman, but also Space Sherrif Gavan. Gavan to this day has operated on earth and in space and has become one of Earth's great heroes.
2004: The Precure were born, starting with Black and White. Officially Heartcatch predates this with Cure Ange, but the first public Precure team was Black, White and Luminous. During this time, Black and White encountered Space Police Dekaranger, and again a year later with Mahou Sentai Magiranger.
This event has not happened in DDD yet.
Confirmed as happened in-canon by Honoka Yukishiro ICly.
2009-2010: Kaitou enters the World Without Riders a few times, during Heartcatch and during the 2009 Era, also encounters Samurai Sentai Shinkenger by stealing Genta's Ika-chan Origami.
2012: Soon after the formation of the Smile Precure and the Go-Busters, the world enters a massive war known as the Superhero War. The Riders and Sentai are working to wipe each other out in a massive battle in the World Without Riders. This event has not happened in DDD yet.