Well... without looking into any side materials, if Xenogears and Xenosaga happened in a single continuity:
- Deus and that whole invasion/terraforming system under his control sounds like something that other Migrant Fleet would create. You know the one - those Ormus dudes. The visual design of the mecha (cyborg?) mooks made by Deus doesn't really match what we are shown of them, if I remember right and there may have been more than enough overly religious people in this Migrant Fleet too, but that's what comes to mind first and foremost.
- This doesn't mean that the ship that was transporting Deus in the prologue is one of those folks though. Neither the crew's uniforms nor behaviour would match if you will leave them unchanged (no turns of speech name dropping 'Lord', 'God', etc, for example) - so conflict between different human factions could be
shoehorned in introduced. (There is a snippet of text in Xenogears that kinda directly contradicts it, but if one wanted to make things more convoluted...)
- Techobabble found in Xenogears would indicate that the method of energy transfer between a 'mothership' and its supporting ships (read: mecha) is only possible via the use of Zohar;
Xenosaga seems to indicate that such things are standart-issue for all military fleet groups euipped to operate with mecha.
Coupled with the fact that Eldridge (a ginormously huge starship comparable to Wilhelm's private death star if I'm not mistaken and supposedly equipped with a brand-new propulsion system that could revolutionize space travel) is moving Deus from an already established facility to another - essentially performing a supply runner's job, not discovery/colonization of uncharted space - it could indicate that Xenogears's prologue happened in quite a faraway past from Xenosaga's perspective when space travel via UMN 'nodes' with travel times and cargo sizes closer to (for an example in our terms) transporting something by a truck, ship or plane instead of sending something to Mars did not exist yet.
Or maybe those people were smarter and didn't conduct terraforming systems' tests and Zohar contact experiments anywhere near any population centers. Or Zohar being the single way to operate mechs and other 'slave generators' is only such because Eldridge's self-destruction system has been effective at its job?
Second Milita is specifically mentioned to be undergoing terraforming still though - and people are already living there normally (at least within the bounds of the population center(s)). Seems like the technology is more widespread and ironed out to me. So it still looks like Xenogears' intro happened either long ago or in a Migrant Fleet cluster completely isolated from what is happening in Xenosaga.
- There is no mention of Gnosis or people disappearing on direct physical contact with Zohar. There are still anomalous things happening around it, but nothing of that sort yet. Could be interpreted as a '+1' to 'it all happens much earlier' idea. Or is it just the Existence that got trapped inside mixes things up?
- Creation of Deus (or at least attempting to hook it up with Zohar) could've been an attempt to make another U-DO, but better. I seem to remember that either the knowledge of what happened to it after humans had to run from Earth or even knowledge about the creation of U-DO overall was unavailable for a long period of time.
- People 'reincarnating' - or at least being able experience memories from their past lives - seems to be only possible because Zohar made it so somehow. It is not something that happens to humans naturally and may even not exist at all outside of the poor planet Xenogears play out on. Same goes for 'Ether' use.
Although, body-surfing was shown to be possible for another individual that survived a Zohar contact experiment - and Dr. Yuriev may have had nothing to do with Xenogears at all. (Unless the good doctor hailed from that part of humanity? And both cases ovserved in Xenogears were performed by people from the batch Deus directly worked on too...)
Apparently the 'main planet' is supposed to be Earth. In that case, it would've been very strange if the crew on the bridge suddnely lost their nerve and captain ordered full evacuation and self-destruction if humanity has already got the hell out of dodge by that point. (And that looks like what had prompted this last option in response. At least in my eyes.) So it places the events in the intro somewhere between excavating Zohar and that unknown anomaly that prompted everyone to run as far away from Earth as they could.
For extra drama one could say that Deus commandeered the ship at the exact same time wierd stuff on Earth started happening, so that was why no one came to investigate the loss of the ship - everybody simply forgot Eldridge in all this excitement or deemed search and rescue operation not worth the effort when survival of the rest of humanity was not certain.
The question is what would it have tried to do if it reached Earth successfully? Would it have accelerated the extinction event and made much, much less of humanity survive the incident? Or maybe it was actually trying to stop whatever the hell was happenning and would've ended up helping humans in the end?