\documentclass[preview,border=1pt]{standalone}
\usepackage{amsmath,amssymb,amsthm}
% Reset to LaTeX's default paragraph indent
\usepackage{etoolbox}
\edef\keptparindent{\the\parindent}
\patchcmd{\preview}
  {\ignorespaces} %%% \preview ends with \ignorespaces
  {\parindent\keptparindent\ignorespaces}
  {}{}


\begin{document}
This is the first paragraph. \\ This is the same paragraph, only on a new line. \newline Still the same paragraph.
\end{document}