Assuming you're talking about the original 2001 Max Payne there is a well known issue that it has problems with audio on versions of Windows from Vista and later. I'm going to assume these same issues have carried over to WINE\ Proton.
Thankfully a user over on Steam made a fix for this problem which patches the sound files so they work properly in later versions of Windows. He also provides sound files which are already patched for download over here. Hopefully these files will fix your issue.
Side note: It would appear the issue is caused by Max Payne using calls to the now deprecated DirectSound API. I'm not sure how WINE\ Proton handles DirectSound API calls, but you may be able to fix this issue by using IndirectSound.
It should work since ages.
Is it fine with latest wine?
I can confirm that lack of DirectSound causes no sound in Quake Live as well.
Edit: Latest QL update enabled DirectSound for the game, thus the game has sound now.
MaxPayne (RU), no sound as well
I can confirm that using IndirectSound mentioned in https://github.com/ValveSoftware/Proton/issues/252#issuecomment-415387882 fixes the issue
For me the game, including sound works right out of the box on Arch
Latest proton update fixes sound problem and some more...
Max Payne starts without sound
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SSE3: Supported
SSSE3: Supported
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SSE42: Supported
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