The APA style covers perhaps a hundred details, not just the titles. To comply with all APA6 regulations, it is best to stick with the apa6 class.
The apa6 class works as advertised and loads all necessary additional packages. See this simple example.
\documentclass{apa6}
\usepackage{kantlipsum}
\begin{document}
Normal Text
\kant[1]
\section{Level 1}
\kant[2]
\subsection{Level 2}
\kant[3]
\subsubsection{Level 3}
\kant[1]
\paragraph{Level 4}
\kant[2]
\subparagraph{Level 5}
\kant[3]
\end{document}

If you want to use a thesis template, you can try Oveveleaf APA6 style manuscript
https://www.overleaf.com/latex/templates/your-apa6-style-manuscript/kngbbqpypjcq
Note that the latest version of the APA dictatorship is APA7, with many changes. Can you see the differences? (Put apa7 instead of apa6 en the former code)

So another option would be
https://www.overleaf.com/latex/templates/template-and-sample-for-authoring-apa7-manuscripts/pvhtwcrvcmsp
Many times, the editorial office of an organization or magazine becomes very picky. Best check with them before issuing your manuscript.
Also, make sure that the template you want to use meets the requirements of the university or department. Many have their own templates. See examples and guidelines in
http://ctan.math.washington.edu/tex-archive/macros/latex/contrib/apa7/apa7.pdf
and most useful (APA 6) from Purdue
https://engineering.purdue.edu/~mark/puthesis/
permanent URL bit.ly/puthesis
From the same source
There is no combination of options that will automatically give proper
headings, tables, and figures according to Publication Manual of the
American Psychological Association, sixth edition, fifth printing,
January 2011. (Informally this is known as the APA format—I call it
APA6.) APA6 specifications are geared toward short papers and journal
articles. It does not specify the format for the table of contents,
list of tables, list of figures, etc. It does not specify the
numbering that should be used for chapters, sections, subsections,
subsubsections, equations, etc
...
The Thesis/Dissertation Office recommends using puthesis.
To test, download the puthesis software and template files, put everything in the same directory, and compile thesis.tex
apa6class for a thesis is probably not a viable idea. – Alan Munn Sep 04 '20 at 21:40titlesecpackage, how should I go about noting that here? – bhnn Sep 04 '20 at 22:01titlesec+ the MDT template, then post an answer here showing what you've done. Self answers are perfectly welcome. – Alan Munn Sep 04 '20 at 22:05