Warning: spoilers ahead for the "In the Name of the Rebellion" episodes of Star Wars Rebels.
Every Star Wars fan worth their spice knows the story of the downfall of the first Death Star, starting with the theft of the plans from the Empire as seen in Rogue One and culminating in the destruction of the whole station in A New Hope. The explosion of the Death Star is one of the most iconic moments in film history, and Rogue One managed to enhance that victory by infusing a greater sense of sacrifice in the mission to obtain the plans. Now, Star Wars Rebels has put a twist on the Death Star story we all knew.
"In the Name of the Rebellion" saw Ezra and Sabine only somewhat willingly joined forces with Saw Gerrera as he tried to attack some Imperial forces disguised on a civilian vessel. The three rebels and Chopper discovered that the Empire was transporting something mysterious in a cargo hold, and Ezra seemed to be hearing something singing through the Force. While exploring, they came across a container filled with scientists and engineers who had been kidnapped by the Empire to work on a project for them, which sounds an awful lot like what the Empire did with Galen Erso in Rogue One.
Ezra and Sabine wanted to prioritize getting the workers to safety, but Saw's mission was not about rescuing some civilians. The trio left Chopper to take care of the workers while they went after the mysterious cargo. Unfortunately for them, the cargo was being guarded by a bunch of Death Troopers, which was an immediate sign that something very valuable was on board. After defeating the Death Troopers, they discovered that the cargo was actually a giant kyber crystal that would be used to power a certain weapon. Harvested on Jedha, the crystal was so large that it was dangerously unstable, and any commotion could set it off and kill everybody on board. Alternately, if the Empire got it to where it was going, it could be used to take a lot of lives.
The rebels ultimately won the day, although it was a close call after Saw betrayed Ezra and Sabine. The kyber crystal was destroyed and Ezra and Sabine were able to rescue all the workers who had been kidnapped to work for the Empire. The workers were all so affected by their experiences at the hands of the Empire that they decided not to return to their families on their home planets. Instead, they wanted to join the Rebellion and use their unique abilities to help the Alliance rather than the Empire. Huzzah for the Rebel Alliance!
If not for the events of "In the Name of the Rebellion," the Empire almost certainly would have completed the Death Star a lot earlier than they did in the existing Star Wars timeline. The Rebels in the movies sustained some pretty massive losses in Rogue One and A New Hope; the death toll could have been even higher if the Empire had completed the Death Star before the Rebels even knew about its construction.
While the Alliance might have simply dissolved in the face of a fully operational Death Star with no means of destroying it, the Empire might have still blown up a planet as a show of force. The planet might not have been Alderaan, but there probably would have been one. Basically, the characters of Star Wars Rebels by destroying the huge crystal and rescuing the skilled workers probably set the construction of the Death Star back long enough for the events of Rogue One to happen and set the events leading eventual A New Hope destruction of the Death Star in motion. The rebels of Rebels bought valuable time against the Empire. Honestly, they probably cost the Empire quite a lot of credits as well.
This isn't the first time Rebels has touched on the Death Star without actually mentioning or showing the Death Star ahead of Rogue One. Back in Season 3, the Ghost crew joined Saw Gerrera on Geonosis, where they tried to piece together what the Empire had done there and what happened to all the Geonosians. They came across a sole surviving Geonosian who seemed to be trying to tell them about the super weapon that had been built in orbit around the planet, but none of the Ghost crew or Saw could understand what the Geonosian was trying to say. If only they had tracked down somebody to translate the Geonosian's language, the Rebel Alliance might have found out about the Death Star well ahead of Rogue One.