How to insert \bigstar in section title with same baseline?

The main problem is that the bounding box of \bigstar is a bit deeper than the actual glyph. On the other hand, pifont provides the correctly sized symbol.

With \DeclareRobustCommand you make the command safe for section titles.

\documentclass{article}
\usepackage{pifont}

\DeclareRobustCommand{\textbigstar}{\mbox{\ding{72}}}

\begin{document}

STAR\textbigstar METHODS

\bigskip

\Large
STAR\textbigstar METHODS

\end{document}

With rules to show the baseline and the top:

With hyperref (thanks to Phelype Oleinik for suggesting):

\documentclass{article}
\usepackage{pifont}
\usepackage[unicode]{hyperref}

\DeclareRobustCommand{\textbigstar}{\texorpdfstring{\mbox{\ding{72}}}{★}}

\begin{document}

\section{STAR\textbigstar METHODS}

STAR\textbigstar METHODS

\bigskip

\Large
STAR\textbigstar METHODS

\end{document}

Here there is my proposal using the macro \basestar and by comment of the user @Zuooo I have scaling the symbol \bigstar with scalerel package. You can increase or decrease the star with the scale factor .7 into \scaleobj.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{scalerel}
\def\basestar{\ensuremath{\mathrel{\raisebox{1pt}{\scaleobj{.7}{\bigstar}}}}} 
\usepackage{xcolor}
\begin{document}

\textcolor{brown}{STAR$\basestar$METHODS}
\end{document}

Here is another method:

\documentclass{article}
\usepackage{lmodern}
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage[svgnames]{xcolor}

\begin{document}

\textsf{\color{Maroon} STAR \raisebox{\dimexpr\fontdimen 22\textfont 2-\depth}{\scalebox{0.8}{$\bigstar$}} METHODS}

\end{document}