IMO the design is bad if it didn't allow for a thicker fan.
Any fan with a decent lifespan has a thicker fan than that, which allows for a longer bushing/bearing inside.
I'm not even talking about as thin as 6mm, 10mm thick fans have poor lifespan unless spinning at very low RPM.
What CFM do you need? How much heat and what temp gradient and all those other relevant specs? The thing is, the thinner the fan, the faster it has to spin, and the worse the lifespan as a result, and the higher the noise.
It seems like you want to do that Impossible Thing, that no matter what existing tech allows, you can't accept that and go down some rabbit hole. Just telling it like I see it. You have to design around what is available and obey the laws of physics. Granted if this is a one-off project, then economy of scale isn't so important as getting this one Thing working well. We might need more details of what this widget is.
I could be overlooking alternative solutions. Does it even need a fan immediately adjacent to the heat source, or can there be chassis or other remotely located heatsinking? 6mm of aluminum can move a lot of heat away to another area. Copper even more. Granted this requires being able to machine it.