- There are those who say that the Dominion controlled the Idran sector despite the Dominion not appearing in early DS9 could the same here (I don't subscribe to that theory my headcanon is that those were independent from the Dominion at time of first contact but were conquered by the Dominion as part of constant Dominion expansion beginning from it's start and continuing to the present and stopped in the AQ). If the Dominion is watching the area where the first part of Prodigy takes place then what would be the best in universe reason why the Dominion doesn't appear in season 1 to dispose of Starfleet vessel and take it's tech? And could the Diviners civilization at it's height have resisted the Dominion?
The Idran sector was not part of Dominion space.
Their 'borders' were quite some distance away.
In the first two years of the wormhole opening in DS9 'Emissary', the Alpha Quadrant species sent expedition vessels to the Gamma Quadrant.
The Dominion didn't like this, so they ended up sending founders to infiltrate the AQ and gather information almost immediately... they simultanously attacked New Bajor, capturing and destroying ships (and captured people) from the AQ side who were in the Gamma Quadrant in those first 2 years ( THIS is how the Dominion managed to modify their weapons so they would be effective against Federation and other AQ species shields... and then the Federation did the same before the War broke out by capturing a Jem'Hadaar fighter - SF analyzed it, and adapted its shields and weapons... but the Defiant was already capable of blocking out Dominion weapons - seems like because it was designed to fight Borg ships, it had more adaptive and powerful shields to begin with).
At any rate, Dominion space may be relatively large, however, I always surmised it was SMALLER than the UFP (especially with Weyoun's comment about what kind of resources it would take to control something as 'vast' as the Federation).
On top of that, the Dominion is a hostile power that spreads via fear, subterfuge and violence. They are more likely to encounter resistance when trying to increase their overall sphere of control... which is probably why they could be smaller than the UFP even after existing for 1800 years before the UFP was founded.
UFP's approach is fundamentally different... and while some species are wary of this and others will hate the UFP for it... on average, it was discovered that majority seems to LIKE openess, sharing, freedom, equality, etc... hence why it has accumulated over 150 member species across 200 years of its existence (and then doubled it by the 31st century - which would indicate the UFP's expansion was slowed down... but size wise, it could have encompassed a LOT of the Milky Way Galaxy... not just 16 000 Ly's for example, or doble of previous estimates. - If the Romulans joined UFP, their former space would then become part of the Federation for example... that's a sizeable chunk from just 1 species... then there are the Cardassians... potentially the Klingons [of whom we hadn't even heard of by the 31st century], etc.).
Also, while Dominion's location in the Gamma Quadrant was unspecified, some maps were drawn by show devs if I'm not mistaken and they placed the Dominion in the upper left section of the Gamma Quadrant (when viewing the Milky Way from the top of a 2D map)... and it was nowhere near the Gamma/Delta border.
Similarly the Gamma Quadrant Wormhole exit was somewhere around the middle of the Gamma quadrant (maybe towards the gamma delta border - but not near it).
The Protostar jumped from Tars Lamora (which was specified by the show writers to be near the border of the Delta and Beta Quadrant) and ended up at the Gamma/Delta border 4000 Ly's away (but was still in the Delta Quadrant).
So, no, from what we know, the Dominion was nowhere near that part of space... unless they experienced a sudden and massive increase in their overall size, but I doubt this would have happened in such a short period of time.
Nothing however says the Dominion never VISITED that portion of the galaxy... but their Warp engines are nothing special (not really faster than UFP... in fact some are slower than UFP ships), so, I don't think the Dominion would particularly be interested in that section of the galaxy... unless something peaked their interests.
As for the Diviner species resisting the Dominion at their height... I have no idea.
We also don't know if they even ENCOUNTERED the Dominion or where the Diviner's home world is.
But to be fair, the Diviner and his technology seem unremarkable... the very fact he needs the Protostar to use it as a 'salvation' of his species to me says they are not as technologically advanced as the UFP nor would they have the resources to resist the Dominion.
The REV-12 is big and suggest a powerful ship... but ANYONE can make a larger and bulky ship and stuff it with plenty of reactors to overpower it (The Scimitar comes to mind - it also depends on how you DESIGN such a craft)... the trick is creating a small ship which has comparable or slightly less overall power... but it would be ridiculously efficient as a result (this is where UFP excells as - making a big thing in a small package... and the fact the UFP was able to develop the Proto-core, suggest a level of technology the Diviner species simply doesn't have and couldn't develop).
It also depends on what kind of calamity befell his species... and could he really use the Proto core to do what he wants it to do?
If its time travel (which is a possibility), then it would fit more or less because the UFP is already embarking on a way towards having mastery of time travel in this era (and we know they achieved it by the 26th century at the latest... but it could have happened earlier because Time Travel already happened for UFP on numerous occasions by the 24th century... its just that at this time they may be developing technologies that would directly set them on that path - and the Proto core could have also been part of that intiia setup).