@shinobinoz Said
You seem to want the religion part to be gone without any of it's effects being accounted for (prior & during). Take that away too & I strongly believe the relationship would have been much better.
Europe at the time was overpopulated, major towns and cities were heavily polluted, many lived in poverty with no hope of change, most of the forests had been destroyed along with much of the wildlife. Then come reports of this wonderful new land blanketed with forests as far as the eye can see. It had pure water teaming with fish. Forests teaming with game. Even the poor now had the chance to improve their lives, whilst merchants saw the chance to grow rich beyond their wildest dreams. All that stood in their way were the native peoples. In order for the Europeans to get what they wanted they had to take from the native peoples. This would have been true regardless of whether or not the Europeans believed in God or if they believed their was no God. So how exactly would the relationship have been much better?
The atheist Europeans would still have brought with them devastating diseases such as smallpox, measles, influenza, and bubonic plague. These diseases killed up to 90% of the native population in some areas. Would this have endeared the Europeans to the indigenous peoples? Would this have ensured a good relationship?
Atheist or not history, and human nature, strongly suggests that the Europeans would have taken the land from the native peoples. How you can invade someone else's land and still have a positive relationship with them i simply dont know. But if you think such a thing is possible then fair enough. That's your opinion.