European disease definitely spread faster than the Europeans themselves did, it’s just not certain what the exact chain of events was. It’s definitely not an area I’m extremely well-read in, but I know there’s speculation that the collapse of complex urban civilizations in what-is-now the USA and Canada may have started before Euro disease started rampaging through, for a variety of factors.

Undoubtedly, though, the massive disease death tolls put some sturdy nails in the coffin.