Borrowing from the excellent indentfirst but reversing the logic, you can try
\documentclass{amsbook}
\usepackage{lipsum}
\makeatletter
\let\@afterindenttrue\@afterindentfalse
\@afterindentfalse
\makeatother
\begin{document}
\chapter{Test}
\section{Test}
\lipsum
\end{document}
There seems to be no consensus on whether or not the first paragraph after a heading should start indented or not, see No indent in the first paragraph in a section?, https://writing.stackexchange.com/q/3152 or https://practicaltypography.com/first-line-indents.html:
A first-line indent on the first paragraph of any text is optional, because it’s obvious where the paragraph starts.
I guess you could argue for both sides. But it does not seem to be an issue that sparks a lot of controversies.
The LaTeX standard classes don't start the first paragraph indented, but indentfirst enables this behaviour for people who want this. Apparently someone thought that feature was worth the ordeal of writing a package for it. Apparently the AMS agrees and also indents the first paragraph.