Mud huts? Rome was composed of mud hut? The tallest building in the world for almost the entire 2nd millenia was in england. Not exactly "mud huts".

https://en.wikipedia.org/wiki/Old_St_Paul%27s_Cathedral

https://en.wikipedia.org/wiki/Lincoln_Cathedral

https://www.businessinsider.com/here-are-the-tallest-buildin...

https://en.wikipedia.org/wiki/History_of_the_world%27s_talle...

I think you are overselling the muslim world and underselling europe a bit.

> the Muslim world had plumbing, water filtration, surgery, advanced mathematics, and many more amazing scientific advances which quickly spread throughout Muslim countries due to the cultural exchange at Mecca.

Much of it brought to the muslim world by the roman empire and the greeks. Or from the indians/chinese/etc in the east. Of course there were muslim contributions but lets not get too carried away here.

> I wonder what the world could have been like if the Mongols had never destroyed so much civilization and progress.

The world would be exactly the way it was in the 1200s without the mongols. The muslim world had stagnated by the time the mongols came around. After all the arabic islamic golden age started in the 700s. The mongols destroy arabic islamic civilization but they helped create the turkic islamic civilization of the ottoman empire not to mention the persian centered khanates which went on to create mughal india. Without the mongols, we don't have the italian renaissance and modern europe and without modern europe we don't have modern civilization. The empire created by the mongols is why marco polo went east. It's also why christopher columbus set sail. Without the mongols, we don't have the new world.

No doubt, the arab world suffered and lost out, but the world advanced immensely due to the mongols. The mongol empire was the first truly "global" empire. It helped europe bypass the muslim world and trade directly with india, china, etc.