*general whole story spoilers.*
"The world forsaken" from the tales from the shadows series the devs posted on the Lodestone a while back tells the tale from the doomed future, where its revealed that the OMG minion has Omega's "consciousness" or something akin to that imparted into it, as it is monitoring and collecting data while narrating events from the doomed future. In it, it specifically mentions that The Tycoon was created through analyzing the encounters with Alexander & Omega, on top of several of the datalogs in the Twinning implying that the NOAH expedition, the group that opened the doors of the Crystal Tower in the CT series, had happened as Graha was already in his stasis state inside the tower, something that directly happens at the end of the CT series and the fact the ironworks peeps from the future didn't have to contend with Xande & the like, as they had already been cleared out. There's also the Tycoon's chamber itself that has portals on the walls clearly depicting moments in time from the Alexander, CT & Omega raids, showcasing they did happen.
OMG even mentions the line "I could by this time emulate the cognitive processes of organic beings, as I had done on one particular occasion many years ago, in the moments immediately prior to the irreversible dissolution of my previous vessel.", directly implicating that the events of the Omega raid had happened. Considering the doomed future begins to happen soon after our current time and the WoL dies in the future one, it leaves a very small timeframe that these expeditions could have happened.
I also believe there's a quote from Yoshi-P or one of the storywriters that they made the decision that all 24 mans & 8 man side-story trials (Warring Triad, Four lords) happen canonically in the overarching story, since it would have limited their ability to use older content to advance the narrative (Tycoon's origins being rooted in CT, Omega & Alexander raids, for example) if they assumed not every WoL went into those instances.
Overall, there's mountains of evidence to showcase the fact that Yoshi-P and his storytelling crew have made the raids & trial stories canon in the overarching narrative, regardless of individual player progress.