Different headheight for first page

You can customize options within the document using \KOMAoption or \KOMAoptions. If you change the layout parameters, \recalctypearea recalculates the layout for you.

Example:

\KOMAoptions{headheight=3cm,headinclude=true}
\recalctypearea
content of first page
\KOMAoptions{headheight=1.25\baselineskip,headinclude=false}
\recalctypearea
\clearpage
further content

Note that you might have to do further adjustments because of the different values of headinclude. If necessary, you can make further adjustments to the textbody using \areaset.

Or consider using headinclude=true consistently in the document.

Write

\AtBeginDocument{\vspace*{2\baselineskip}}

or, simply

\begin{document}
\vspace*{2\baselineskip}

The first form is more suitable if you're preparing a personalized .sty file. Change the 2 into what is best for you.