When the show was announced and concept art was released, there was a lot of concern among adult fans that it would be a "kid-ified" version of the series, with all of the action and drama toned down and replaced with comedy. Steven Spielberg himself assured fans that this was not the case, and indeed the show sticks pretty close to the tone of the movies, with the only things "toned down" being the presence of blood and the use of profanity.
The kids run into the crashed gyrosphere of Zach and Gray from Jurassic World, who were forced to abandon it after their first perilous meeting with the Indominus Rex. They also see the corpse of the ankylosaurus that the Indo killed.
When attempting to escape the park, the gang discovers the "Jurassic Park River Adventures", a reference to the Jurassic Park ride found at Universal's Islands of Adventure. The canoes that they ride are even the same color yellow as the ride vehicles found in the real life park.
The chatter over the walkie-talkies reveals something specific about the fate of Dr. Wu from Jurassic World (2015), who was implied to have survived the Indominus Rex attack and escaped offscreen (confirmed by his appearance in Jurassic World: Fallen Kingdom (2018)). Guards are heard crying, "Shoot her!" while the sounds of velociraptor noises are heard. One guard shouts, "The order is to save Wu," further indicating that making sure Dr. Wu got off the island was of paramount importance, no matter how many raptors (or other "assets") were harmed. The chatter indicates the brutal circumstances surrounding Wu's perilous escape.
After Kenji and Darius mistake a Velociraptor paddock for the Compsognathus pen, they encounter four raptors ready to make them a midnight snack. They end up escaping thanks to the quick-thinking of the staff and spotlights, part of an elite group of individuals who have faced raptors and lived to tell the tale. As they're being pulled from the gates, a familiar raptor makes a quick appearance. Eagle-eyed fans will immediately recognize Blue, Owen Grady's favorite raptor companion and hero from Jurassic World (2015). She also makes an appearance at the end of the first season before the credits roll.