I like the fair and constructive tone
@Infinity and
@Skallagrim have added to the thread.
I agree that European discovery of the americas could be delayed by a lot if we allow for early enough PoDs.
Going back to the OP: he really asked WHAT WOULD HAPPEN then. And that depends on the PoD, as I said. If, for example, we go with the open Eurasian trade routes, we might well delay a century or two without changing, say, climatic conditions across the Atlantic, and when the colonisers finally reach the Americas, they'll behave recognisably from an OTL perspective.
So, in this scenario we can simply attempt to simulate how native American history would have developed along the paths we know something about.
If, on the other hand, we're postulating that Europe remains way less developed, that might mean more forests, would that already be enough to change climatic patterns as far as America to a significant degree? I don't know...
Yup, this is one of those cases where the "how" decides the "what". Giving that some thought, the "easiest" way I can see to tie Europe into the rest of Eurasia is (somewhat boringly!) a Christianity-wank. Prevent Islam from rising up, giving Christianity a lot of good luck, and have some Persian ruler go the way of Constantine. Christianity takes Persia (or at least becomes very strong there), has inroads deep into Asia, etc. etc. -- The wide expanse of this alt-Christendom makes a united Church nearly impossible, which may be good. Imagine a far more decentralised Christianity, with various sects and rites all over the place. Without central authority, they mostly just co-exist instead of fighting senseless wars of religion.
Effects: the ancient Rome-versus-Persia divide finally ends, as both are now within Christendom. Additionally, Europeans become primarily interested in spreading their religion into Eurasia, which turns their gaze east and land-inward. Finally, the absence of islam might just mean that certain texts preserved by islamic scholars get lost in this ATL? This one's iffy, becauase "no islam" can just as easily mean that they are preserved in the ERE. Then again, that's not a given. For the sake of the scenario, we might imagine that the ERE goes through a pretty fanatical Christian phase and burns a lot of "pagan" books. It wouldn't be the first time. A result could be that some classical knowledge is lost, which sets the Christian world back just that little bit compared to OTL. Seems petty, but we need everything we can get to keep them from discovering the Americas!
That would be the most straight-forward scenario, I think. It allows for history in the Americas to go on as per OTL, I'd say.
A problem would be that people are just going to figure out the size of the world, and realise there's a huge unexplored part. Eventually, someone will go looking. Then again, before 1492, China showed no interest. Even after, when they surely learned of America's existence via the Europeans, they evinced
no desire to go colonising there. (The first real Chinese presence in the Americas was the influx of labourers as of the 1820s.) So it
is entirely possible that something like Vinland happens in this "Eurasia-focused Europe"-world... and nobody cares. Perhaps it happens somewhat like in OTL the first time, and nobody even really notices. Then someone else stumbles upon America later on... and while this is noted in Europe, nobody really cares. Especially if they manage to miss the more developed civilsations of Mesoamerica. The "Western barbarian isles" (or whatever they'd consider them to be) would just not be very interesting.
Eurasian civilsations
did make major inroads into Indonesia (Hindus first, Muslims later). I could see a Eurasian Christendom esxpanding much like Islam did in OTL: going down East Africa, and across the Indian Ocean. It would be funny if they eventually discovered the Americas from the
west, after island-hopping their way through Polynesia!
Regarding time-frame: if we compare the spread of Islam into Indonesia, and compare to a hypothetical Eurasian Christendom and its spread, those might just be similar. So... flourishing of Christian Indonesia around 1500? Trade routes to the East well-established, no need to go looking for another route... Add a long period of vaguely exploring the Pacific (took some 300 years in OTL), with a convenient detour involving Australia (and New Zealand?)... Well, by that point you
can in fact end up past 1800 before Eurasians reach the Americas in the first place.
It's far from a given, but it's not ASB.