The only way I know of to do this is to mute your Mac's volume right before you turn the machine off. With volume muted, the machine will not do the start up noise. You can then unmute for the remainder of the time you are using it.
Check out this, and
AppleScript tutorial
will help with a search engine. Macscripter.net (listed in the link) is a site worth visiting, though it may be a bit daunting, here and there.
Macscripter.net has been around for ages, so if you're looking for a script's particular function, whatever you find may or may not work in your version of AppleScript. Some of those scripts are ancient, though they may have been updated to suit the newer syntaxes.
In the meantime, try pasting this one-liner — or any other — into a new Script Editor window, and click on Play. Or save it as an application and add it to the log-in list.
say "hello, my good and excellent lord and master of the universe."
I use this preference pane. It's free. It probably just makes volume changes when shutting down, and then when logging back in, but the result is your computers user-defined volume remains the same, and the startup volume remains at a user-determined level as well.
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