I have done some thinking of what a Warframe/Babylon 5 crossover would look like. One key aspect of the story is that the Tenno must not be point of view characters.
I think for the most part, the Corpus would make a decent substitute for the EA, especially after reforms pushed by an alliance of Parvos Granum, Perrin, and the Tenno. Without video-game stasis, the Tenno would focus on breaking up the Grineer by permanently killing the Queens and assassinating key leaders. Then the Fragments of the Grineer would mostly be absorbed by Steel Meridian, Tenno aligned Kuva Liches and Kavor. However some independent Grineer remain as pirates and raiders.
Into this settling chaos stumble the Centauri, who instantly recognize that the overpopulated star system would have a high demand for FTL travel. In this timeline the Centauri do not attempt the same tricks they did OTL, instead they try and make the Origin system dependent on them for FTL travel. Leasing jumpgates and jump capable star-ships, but never selling them.
This gambit earns the Centauri great profit, but eventually falls apart. Solar rials are perfectly capable of being used for interstellar travel as long as you can get one to your intended destination. The mysterious Tenno are also adept spies and highly intelligent, thus the first hyperspace capable ships built in the Origin system would be Tenno carriers and soon after the jump drive would be produced for the Corpus by the Perin Sequence. It is assumed by many that the Tenno sold Jump Drive technology to Perin in return for help producing capital ships. Due to Tenno stealth technology, no one actually sees a completed Tenno Carrier until much later.
The Dilgar war goes much like OTL, with the Corpus taking umbrage to Dilgar attacking their trade ships. However the exact details are different due to the Corpus being much more technologically advanced than the EA, and there is a major indecent Jha'dur acquires technocyte samples from Grineer pirates, resulting in a major Tenno intervention.
The Anlo'Shock voice their growing concerns about the mysterious Tenno and the Technocyte to the Grey Council of the Mimbari. The Anlo'Shock incorrectly believe that the Technocyte is a shadow bioweapon or derivative there-of. Likewise the Tenno's stealth technology reminds them of the Shadows ability to fade in and out of hyperspace. The Anlo'Shock are able to present sufficient evidence that the
Grey Council orders a more overt investigation into the Corpus and Tenno.
What they find is confusion and contradiction. There are few who know any details about the Tenno, and the only ones who managed to survive to the point of the Mimbari's investigations are the Tenno's allies. For every praise of the Tenno as saviors, they are rumors of them being demons, monsters and betrayers. The chaos does not play well with the Mimbari's ordered mindset and occasional attacks by Grineer raiders infuriate them. Worse yet, the Vorlon take interest in the investigations of the Mimbari, they have few words for the Mimbari, only describing the Tenno as "Unknown" and the Technocyte as "Abomination".
It is the Vorlon's presence that finally draws out the Tenno to speak. It is upsetting to the Mimbari that the Tenno treat the Vorlon as equals, demanding reciprocity from the Vorlon in order to show their true face. Talks break down then the Vorlon attempt a psychic probe, and the Tenno retaliate.
The Vorlon do not commit to the resulting conflict, leaving it to their Mimbari puppets. The trust they place on the Mimbari's seniority soon is revealed to be a mistake. The Corpus are quite capable of fighting the Mimbari on an equal footing and Tenno are spotted on Mimbar in short order. There are rumors of Vorlon actions during the war, but they are unwilling to act overtly.
The Corpus see little profit in continuing the war, thus the Terms of surender offered to the Mimbari while humbling are not harsh. The Corpus not wanting further diplomatic incidents causing unprofitable wars demand the Minbari and politely request the Tenno help them construct a diplomatic station in neutral space. The Tenno respond with great enthusiasm and provide psychic dampeners and other esoteric defenses for the station.
The Tenno also seek out additional factions to send diplomats. Thus, when Babylon Relay is opened, it is greeted by a Murex, a Shadow Yatch and a Vorlon cruiser. This is also the first time any of the younger races has seen a Tenno carrier.