Does this Nebula Cosmos Laser 4K have a port labeled ARC? Or an optical out port?

Yes HDMI supports ARC

Then connect the Beam to that HDMI connection. Connect all your input devices to the HDMI switch, and connect that to any HDMI port not labeled ARC on your projector. The Beam will then play anything your projector is showing. 

Sorry I am not following I connect the beam to the input on the matrix then run another hdmi from the output to the projector 

the projector only has one hdmi port

i tried what i wrote above and it did not work 

The only other output I have on the projector is a aux jack 

I don’t think the projector is equipped to work with a home theater system :(

With one HDMI port, I’d agree. 

You could go the more expensive route, and get an external device to create either an optical output (Dolby digital at best, connecting to the Sonos optical adapter, which connects to the Beam. Those are relatively inexpensive. The other, more costly option is an external ARC device. 

There is the HD Fury Arcana, the Feintech VAX04101k, and the OREI HDA-935. You can also order from those links from the companies directly, or check your local retailers for availability. Amazon may carry some, depending on location. At this point, there may be more manufacturers, I haven’t been keeping track.

One of those would then connect to the Beam, and your matrix switch could connect to it.