I think it's effectively impossible without a very early POD. A few possibilities.
If the Americas has more of its own animal domesticates, it's plausible that all conditions would be met. More domesticated animals means more protein sources, and possibly beasts of burden. If American horses survive, it will greatly help the dissemination of technology as well. And exposure to domesticated animals should build more disease resistance.
The problem is, I don't buy Jared Diamond's idea that it was solely lacking domesticates that the Native Americans suffered so greatly from plagues in the post-Columbian era. While hunter-gatherers worldwide always suffer from plagues, the record is more mixed for agriculturalists. Papuans, for example, independently domesticated plants, and when Austronesians introduced pigs to Indonesia, they didn't seem to have any major epidemics, and faced no population replacement. Similarly, there were no major epidemics which were caused when Europeans landed in New Guinea. On the other hand, European diseases wreaked a pretty bad toll on some Polynesian islands, despite the natives having access to dogs, pigs and Chickens as disease vectors.
What I think it comes down to is Polynesians were inbred to some degree, while Papuans were not. Many Polynesian islands were settled, after all, by a fairly small founding population. The Americas is similar, insofar as the first wave of Native Americans has been estimated to have been a group of less than 80 people. Later migrations by the ancestors of Na-Dene and Inuit into the Americas diversified North America a bit, but not tremendously.
Still, the issue is, Native Americans are far more similar genetically, even after thousands of years of mutations, than populations in the old world. Related to the immune system, this is big trouble. A genetic weakness for one variant of flu, for example, is highly likely to be shared across virtually the whole population. Essentially, Native Americans could have been the human version of the Irish Potato Famine. Thus while more domesticates might help a little bit, you're still going to get a "great dying" when Eurasia comes a calling.
One way around this is to introduce Eurasian DNA fairly early, and then let contact lapse. A possibility I prefer is Carthaginian/Roman contact. Say there's enough to establish a self-sustaining beachhead with Iron Age technology somewhere in the Americas. The plagues, of course, happen. But contact is also cut off with the outside world when the home country goes to pot, so there is no chance of widespread colonization. Instead you end up with a hybrid "mestizo" culture forming right around the original colonies, with progressively less cultural and genetic influence as you move further from the old colony sites. But you'd still get some - even modern day Mayans and Quecha are around 5% European. 1500-2500 years is more than enough time for natural selection to work its way through the population, and you'd end up with a plague-resistant, mostly Native American population.