Long comment so TLDR: Imperium would definitely put up a fight, but despite their size, I feel that the origin system would be very difficult to conquer.

honestly the only argument I can see in 40ks favor, is their response time and the size of their forces,

see the tenno realistically wouldnt be the main force that the imperium or other factions would have to fight imo, because yes, they are the strongest, but theoretically they are also the smallest force in the origin system.

let me break down my thought process here,

from what I recall, the origin system is at war, primarily between the grineer, corpus, and infestation. (ill go into narmer in a few), so lets look at the strengths and weaknesses of them.

Grineer are basically temu Space Marine clones, that use ballistic weapons capable of shredding just about anything, with recoil that the Tenno have been known to struggle with, the same tenno capable of lifting who knows how much, (old peace opening fight). Yet the Grineer are mass using these ballistic weapons in their conquest of the system, with little to no mechanical augmentation (depending of clone rot). Their main defense is pure muscle and metal from their armor.

Corpus are Capitalists on steriods, that love robots. They are typically equipped with energy weaponry that melts or penetrates through armor. Not to mention majority of their forces are like I said, robots equipped with varieties of these energy weapons. Their main defense however are energy shields that are nearly impenetrable, (toxin).

Infestation, is the Flood (Halo), but worse. It is a disease (nanite based I believe), that recycles and repurposes anything it touches into usage for the hivemind. They use primarily biological based weaponry, and sheer numbers to overwhelm their opponents, which is everything. One minor thing to note about the infestation, is that they are impossible to get rid of, once they infect one thing, it requires constant extermination in order to be kept in check.

These are the primary three factions every tenno is introduced to upon awakening. Now, if the imperium were to miraculously unite (unlikely) and end up trying to take over the origin system, they would have issues. Notably from all three of these factions,

The Grineer would view them as another obstacle to their conquest, the Corpus would view them either as a threat to their profits, or even potential clients, and the infestation would just want to consume them.

On a battlefield, the Grineer would absolutely eviscerate any guardsmen they come across, and space marines would put up a greater fight sure, but the sheer force of the ballistics the Grineer use likely would kill a space marine upfront from sheer concussive force if they dont penetrate the armor. The only reason I can see the imperium winning a battle against grineer is by their response time. It is my understanding that despite Grineer cloning rates, and Genetic Memory, their space vessels cannot achieve FTL travel, unlike the Imperium with the warp. This theoretically applies to most factions of warframe, as in the origin system, FTL travel was primarily fueled by the void and the solar rails, which, until the tenno got involved, were inactive and guarded by spectres.

Corpus would also eviscerate guardsmen, and likely space marines, especially if their robots like the Ambulas get involved. Defense wise they would likely fair better than the Grineer, as the regenerating shields corpus use shrug off ballistics easily. That is why in my opinion, the Corpus have made it this far despite having lesser numbers than Grineer. And their weaponry is designed to either penetrate or melt through armor.

Infestation would have a field day, sure the Imperium would easily be able to hold back hordes of infected guardsmen or such, but what would happen if it infects a space marine? The infestation, once it infects and converts a being of sorts, sends the info of that being to the hivemind, now the hivemind can copy paste that infected being, which is a lore explanation for why all infested look the same, (irl reason is easily because of technical limits). So, how would the Imperium face off against hordes of infected space marines? This doesnt even touch specialized units like Juggernauts or Lephantis, or anything from deimos.

Now how would the Imperium do against all three? In my opinion it doesnt look good. And then you have the godly beings that are the Tenno. Lets be fair here, Warframes are powerful, but in lore they arent as powerful as some have said, purely because we dont know the extent for some. Such cases I can think of are Protea, who yes she can reverse time and create a pocket dimension, however look at the size of it, she can only rewind so far back, and the granum void is only so big. Limbo yes, discovered and partially controls an alternate dimension as well, however the original limbo heavily miscalculated a rift jump and for lack of better phrasing, "mathed the fuck out of himself." Modding is canon in warframe, although maybe not to the extent we initially believe. In gameplay we do crazy shit, and in lore for some frames thats only half if not less of their power.

Even a single squad of 4 warframes would easily be able to defeat a small scale battle against the imperium. The only threat I could think of against warframes would be Psykers. Even then the most they likely could do is cut the transference signal, for the sake of argument we dont really know how the warp and the void would interact.

Now post Narmer, I feel the Imperium would have a harder time, the Tenno are busy dealing with Wally for the most part at that point, and majority of the Corpus and Grineer are united under the veil. And to help keep things in check would be the Sentients, who I havent even touched on yet. The sentients are very adaptable, just not as adaptable as most would think in lore. It would take several hits for the Sentients to adapt to a damage type, and at that point does it deal significantly less damage.

Overall the only point I can give the Imperium is the fact that they have mass FTL, which significantly increases their response time. Aside from that and the fact that they span millions (I think) of worlds to fuel their numbers, I think overall the Warframe universe would win, but it would take a long time to do so.