This presupposes that such convincing is even possible. Many, many companies have leadership that are simply terrible at identifying value. If you've never been part of a majority of developers advocating for, if not outright begging for, some huge ROI initiative to get the green light, you are very fortunate.
There are great counterexamples, like Valve, which is known for giving developers an extreme degree of autonomy, and they benefit greatly from that approach. For each Valve, though, there are dozens of companies that manage to succeed despite themselves.
Take Microsoft, for example. One tiny, yet representative, example: the way the Windows Terminal team handled a suggestion from Casey Muratori to take their software from abysmally slow to lightning fast:
https://github.com/microsoft/terminal/issues/10362
A quote from one of the Terminal developers, dismissing the suggestion:
> I believe what you’re doing is describing something that might be considered an entire doctoral research project in performant terminal emulation as “extremely simple” somewhat combatively…
Just how difficult was such an endeavor in actuality? Well, given that Casey implemented his own terminal emulator from scratch and incorporated the functionality he was proposing in a mere weekend... not a whole lot. Relatively minor effort for a huge return on investment. It took Casey explaining the concepts, then providing a working proof of concept, and finally a bunch of backlash online towards the Terminal team to get them to do the right thing for themselves and their users.