I'm a bit confused by how the question is formulated but let me give it a try to answer you:

Since you are referring to the inentionalism-functionalism debate, I assume you are asking what evidence the intentionalists brought forth for their interpretation of the process that lead to the Holocaust.

The first thing that is important to understand this issue, is that the intentionalism-functionalism debate was more than a debate of the question what lead to the Holocaust, it was also very much a debate on how to write history. As the most prominent intentionalists Klaus Dietrich Bracher, Eberhard Jäckel and to a lesser degree Klaus Hildebrand all belonged to a school of historians that was much more old school in their understanding of how history works and is written. All of them are very prominent writers of diplomatic history and the history of international relations. Their view of history was one of the primacy of politics, as in political decisions made by important people shaping history more than anything else.

On the other side, the functionalists such as Mommsen, Broszat, and Adam all came from the newly established field of social history. They emphasized structures such as class relations, power relations, institutional actors as the shaping force of history, which pretty much straight-out contradicts the older paradigm Bracher et. al. were pushing.

This is important to keep in mind because it means that the same evidence will be interpreted differently depending on who is doing the interpretation. Case in point:

The T4 program. Instituted in 1939 the T4 program aiming at murdering certain groups of handicapped people was - and remains today - seen as an important precursor for the Holocaust by both sides in this debate. However, while functionalists would argue that once the program had to be stopped due to public protests, structural logic demanded that a new field of work had to be found for the experts in murdering people brought up by this program and thus the idea to kill the Jews developed, intentionalists would argue that this was a precursor, a test case for what was to become reality later. Both of which can be supported by a historical argument since when the Nazis talk about eliminating Jews or the Jewish influence or finding a final solution for the Jewish question, what they mean can only be inferred from what they do or what they say.

And while functionalist focus more on what they do, intentionalists will focus on what they say more, especially on what Hitler says since in an intentionalist interpretation of the Holocaust, Hitler will play the major role while functionalists while focus more on institutions and their cooperation. Bracher and Jäckel both cite Hitler's writing in Mein Kampf as well as the famous 1939 prophecy speech in which Hitler said that once World Jewry would start another world war he would annihilate them. Other evidence they might cite is the Göring to heydrich document in which the former entrusts the latter with preparing a final solution to the Jewish question in 1941.

Another thing, intentionalists will cite as evidence for their case is that it is pretty clear form early on in Nazi rule that they are preparing for a war. At the latest in 1936, Germany will fight a war somewhere in the near future just because of their economic policies. Assuming an important connection between war and genocide, intentionalists will say that with the war, they already planned physical annihilation.

Generally - and thankfully in my opinion - this debate has been over since the 80s and the general consensus seems to have become a middle ground accepting points from both sides of the debate. Today, historians will agree that Hitler played a more central role than functionalists afford to him but that also while a plan of eliminating Jews was in place from the very beginning, the form that would take was not and that the idea of physically murdering them developed only over time and through the factual and practical constraints the functionalist like to emphasize.

Sources:

• Kershaw, Ian. Working Towards the Führer: Essays in Honour of Sir Ian Kershaw, edited by Anthony McElligott and Tim Kirk, Manchester University Press, 2003

• Ian Kershaw: The Nazi Dictatorship. Problems and Perspectives of Interpretation, (London, 1985, 4th ed., 2000).

• Ian Kershaw: The 'Hitler Myth'. Image and Reality in the Third Reich (Oxford, 1987, rev. 2001).

• Karl Dietrich Bracher: Zeitgeschichtliche Kontroversen um Faschismus, Totalitarismus, Demokratie. Munich 1976.

• Eberhard Jäckel: Hitlers Herrschaft. Vollzug einer Weltanschauung. Deutsche Verlagsanstalt DVA, 4. Aufl. Stuttgart 1999.

• Martin Broszat: "Hitler and the Genesis of the ‘Final Solution’: An Assessment of David Irving’s Theses"" pages 73–125 from Yad Vashem Studies, Volume 13,1979.

• Hans Mommsen: Der Nationalsozialismus: Studien zur Ideologie und Herrschaft (Studies in National Socialist Ideology and Rule), co-edited with Wolfgang Benz and Hans Buchheim, 1993.