You haven't produced a MWE that demonstrates what you want solving so I have not tested it or produced MWEs.
a) If all you want is to shift the header you could add \usepackage{needspace} and then put \needspace{5cm} before your section header
Best to hard boil this into your heading settings for example
\usepackage{needspace}
\usepackage[explicit,pagestyles]{titlesec}
\titleformat{\section}{\needspace{10\baselineskip}\color{headcol}\large\sffamily\bfseries}{\thesection}{1em}{#1}[]
\titleformat{\subsection}{\needspace{7\baselineskip}\color{headcol}\large\sffamily\bfseries}{\thesubsection}{1em}{#1}[]
\titleformat{\subsubsection}{\needspace{4\baselineskip}\normalsize\sffamily\bfseries}{\thesubsubsection}{1em}{#1}[]
b) If you are trying to control orphans and widows within the list
You could do something like this. Pick your penalties at each level.
\documentclass{book}
\usepackage{enumitem}
\newlist{myfinelist}{itemize}{7}
\setlist[myfinelist,1]{}
\setlist[myfinelist,2]{beginpenalty=5000}
\setlist[myfinelist,3]{beginpenalty=5000}
\setlist[myfinelist,4]{beginpenalty=5000}
\setlist[myfinelist,5]{beginpenalty=5000}
\setlist[myfinelist,6]{beginpenalty=5000}
\setlist[myfinelist,7]{beginpenalty=5000}
\begin{document}
\begin{myfinelist}
\item[•] Hello Hello
\item[•] Hello Hello
\begin{myfinelist}
\item[•] Hello Hello
\item[•] Hello Hello
\begin{myfinelist}
\item[•] Hello Hello
\item[•] Hello Hello
\item[•] Hello Hello
\item[•] Hello Hello
\item[•] Hello Hello
\end{myfinelist}
\item[•] Hello Hello
\item[•] Hello Hello
\item[•] Hello Hello
\end{myfinelist}
\item[•] Hello Hello
\item[•] Hello Hello
\item[•] Hello Hello
\end{myfinelist}
\end{document}
\usepackage[avoid-all]{widows-and-orphans}
work for you?