I am going to make an educated guess using my knowledge of Islamic history, so it while it may be flawed, this is what I always imagined this scenario would've played out as:

While it is known that Islamic civilizations after the death of the Prophet (SAW) were not perfect, Islam was still very tolerant, and overall, less aggressive.

If Islamic civilizations reached the "New World" before the Christian world did, I believe that it would have played out the same as when Islamic civilization reached Indonesia and such, in which, instead of being violent, we traded with the local natives, and created trade routes and such.

Overall, it would have been much more peaceful, and there would've been a lot more mutual respect and more trading between the two worlds (Old and New), especially with how peaceful, equal and fair Al-Andalus was, along with the hospitality of the Natives

And of course:
Please don't cite me, there are plenty of experts out there who have degrees, this is just my take.