Probably not. First of all, I assume you mean the first European, as we all know there were millions of people living in North, Central and South America as well as in the Caribbean (where Columbus landed in the Antilles) for thousands of years.

Modern fact-lovers like to reference Leif Erikson, who was probably one of, if not the first, European to set foot on North America (possibly at L'Anse aux Meadows in modern day Newfoundland, or around the Gulf of St. Lawrence, either way there was a settlement according to Icelandic saga). Erikson is credited with establishing the settlement of Vinland here.

Erikson was motivated to search for what would become Vinland by a merchant named Bjarni Herjolfsson who claimed to have spotted land west of Greenland after being blown off course in a storm (Erik the Red, Erikson's father, founded the Greenland settlement). Erikson, while traveling to Greenland to convert them to Christianity, was also blown off course. One source says that he rescued two shipwrecked men on land and returned them to Greenland. If this is to be believed, these may be the first Europeans to set foot on NA.

Regardless, Erikson took a ship with 30 men to look for the land, he made at least two stops on the way before deciding to overwinter in what would become known as Vinland. Helge Ingstad and his wife Anne Ingstad discovered the partial remains of a Viking-era settlement at L'Anse aux Meadows in the 1960s, confirming conclusively that the Norsemen had reached NA as early as 1000 AD. Ingstad also believed that the sudden disappearance of the long-lasting Greenland settlement was a result of Greenlanders emigrating to North America for more hospitable conditions.

The Saga of Erik the Red specifies two other settlements existed around Vinland: Straumfjoror and Hóp, even further south.

It is not known how long Vinland remained active, probably not very long judging from the texts. There is, however, evidence that Greenlanders used Markland (another area of North America, north of Vinland) as a source of timber for perhaps another few hundred years. In the Icelandic Chronicles there is reference to a ship arriving in Iceland in 1347 after having been blown off course on its way from Markland to Greenland with a load of timber.

No matter, it is safe to say that dozens, and perhaps hundreds of Europeans had landed in NA at one time or another between 1000 AD and 1492 when Columbus reached the Antilles believing it to be Asia.

Here is a map to give you an idea:

https://upload.wikimedia.org/wikipedia/commons/6/6c/Erikr-eng.png