This is a few years old, but I saw it when it landed back on the front page, and it deserves an answer. Actually, it deserves two, depending on which problem you want to solve: getting those accents in Garamond, or faking accented characters in a font that does not contain them.
You update in the comments to say that you ended up using Linotype Garamond Premier. In 2020, a free font that contains all these characters is EB Garamond. Garamond Libre would also work.
\tracinglostchars=2
\documentclass[11pt,twoside,openright]{book}
\pagestyle{empty} % Suppress page numbering.
\usepackage{polyglossia}
\setdefaultlanguage{esperanto}
\usepackage{ebgaramond}
\begin{document}
Antaŭparolo
Ĉi-loke estas kaj fariĝis ŝoseo estas ŝtopita teĥnike
\end{document}

If you are looking instead for a solution to the problem that your font does not contain combining accents (rare these days, but I have run into it), you can tell LaTeX to use non-combining accents. A MWE for your sample:
\tracinglostchars=2
\documentclass[11pt,twoside,openright]{book}
\pagestyle{empty} % Suppress page numbering.
\usepackage{polyglossia}
\usepackage{newunicodechar}
\setdefaultlanguage{esperanto}
\usepackage{ebgaramond}
\DeclareTextAccent{\^}{\UnicodeEncodingName}{"02C6} % Modifier letter circumflex accent
\DeclareTextAccent{\u}{\UnicodeEncodingName}{"02D8} % Spacing breve
\newunicodechar{Ĉ}{\^{C}}
\newunicodechar{ĝ}{\^{g}}
\newunicodechar{ŝ}{\^{s}}
\newunicodechar{ĥ}{\^{h}}
\newunicodechar{ŭ}{\u{u}}
\begin{document}
Antaŭparolo
Ĉi-loke estas kaj fariĝis ŝoseo estas ŝtopita teĥnike
\end{document}

The Unicode standard says that canonically-precomposed and decomposed characters should be equivalent, but not every font on every system implements that correctly. If a font you want to use contains combining accents, but a precomposed character does not work, delete the \DeclareTextCommand
lines from the above example.
\^ o \^ g \^ h
I get ô g h, in other words it puts the accent over o but not over g and h.