If a program is executed for the first time in Windows 7, it automatically hides the icon. Is there any manifest setting or option to force Windows 7 to always show the icon
It's certainly not "impossible". There is an undocumented COM interface ITrayNotify for retrieving tray icons and changing their visibility, used by Explorer itself. Full C++ source here: http://thread0.me/tag/windows/
Of course, using an unofficial API is risky and Windows 8 has intoduced breaking changes to this API, which means you have to use 2 different definitions for XP - Win7 and Win8 - Win10. But hey, even Chrome uses this trick. Just be sure to handle failures properly.