The Spanish and Portuguese noticed early in the 16th century that the native peoples of the Caribbean and South and Central America were sickly to the point of being unsuitable (in general) for slave labour. From this the First Atlantic System develops into South and Central America:
Regarding the Atlantic slave trade
[The First Atlantic System] started (on a significant scale) in about 1502 and lasted until 1580 when Portugal was temporarily united with Spain.
...
Native peoples were at first utilized as slave labour by Europeans until a large number died from overwork and Old World diseases.
So to answer your specific question - By 1502, just one decade after Columbus' arrival in the New World
A comment on the original question states:
I don't think you can expect a reasonable answer to this. Some Europeans might have noticed something, as in Pieter Geerkens' answer, but it's not really understandable at least until you develop the germ theory of disease, and probably not until you start to understand the immune system.
I believe this conflates cause - viral and bacterial agents unknown until modern germ theory - with effect - that the indigenous people of North America were at (greatly) increased risk of sickness. That the effect was known - and widely so - is evidenced by the rapid adoption of race-based slavery around importation of black slaves. Employing native labour would have been more convenient and less expensive - except that the native peoples were too sickly to be so employed.
However - the distinction between Old World and New World diseases was meaningless until modern germ theory. Prior to that realization diseases were classified solely by symptoms and not cause - as the causes were both unknown and misattributed.
