In 632 the prophet Muhammad died, which serves as the most rational starting point for Islam as the religion we know of today, as Muhammad's life teaching are the second most important source in Islam (after the Quran), and his life teachings logically ended when he himself died.
The Anatolian part of Armenia, which is often considered to be Europe, was partly conquered by Islamic forces in 638. The Caucasian part was conquered by 645.
Cyprus, current member of the EU, was conquered by Caliphate forces in 649. Other Mediterranean, European islands such as Rhodes soon followed suit.
The Iberian peninsula was conquered in 711.
So, depending on your definition of Europe, it took Islam anywhere from 6 to a maximum of 79 years to make inroads into Europe.
What's more is that since these particular campaigns, Islam has NEVER left Europe.
>Armenia was under the rule of the Caliphate from 638 to 880
>Iberia was under the rule of the Caliphate from 711 to 1492, and had a small (crypto-) Muslim presence until 1727
>The Ottomans held one of the largest territories in Europe (only second to communists) from 1354 to arguably today (with Turkey having 3% of its territory in Europe and being the respected successor state to the Ottoman/Roman empire), and inarguably until WW1, and the European Muslims who were converted by the Ottomans still exist, in the millions.
This means that since the first Caliphates made inroads into Europe, there has been a continuous Muslim presence in the continent.
And this is why Islam is a integral historical part of European culture.