Make it as organized/structured as possible. Go through the social initiatives arm of the firm, if they are big enough to have one. To them "our social responsibility initiatives" or "open source community contributions" sounds better and webpage-worthy than "we pay project X, Y and Z" (even though that is basically what it boils down to).
On the other hand, for a smaller firm, this might probably be just a one-to-one talk/convincing an executive. If you can't convince one, try another. If you can't convince any, take it as a flag with the color of your choosing.
I'd love to help you build out that business case & open source it. Let me know if you're interested https://discord.gg/fQGqvQdWxq We're also started sharing interviews with maintainers who talk about the people aspect of what this funding means to them https://www.youtube.com/@thanks_dev
Tell them it is risk management; funding OSS ensures that projects you depend on will exist as OSS into the future and hopefully have less bugs and security problems.
