I am using the adobe font "Soleil" for my company branding, but I am not able to use this font for different programs or documents, for example Google G Suite. Has anyone here been through the same situation, or can someone help me solve this issue?
Here I can't find any Adobe Fonts, for instance Google docs.
Adobe Fonts are installed for the apps on YOUR COMPUTER. Google Docs runs entirely in Google's cloud, it cannot use the fonts in your computer. You need to distinguish between local apps (like Notepad, Photoshop) and cloud apps (like Google Docs).
Thank you very much for your help! Do you know if there is any way I can hack this? I also heard about this free add-on for Google Docs called Extensis Fonts.
No, you can't use any kind of clever font manager because Adobe don't give you the font files which the font manager would need. Google do have a very large collection of fonts, you should look at that because that may be the only choice you have.