mac mini 2018 no recognizing monitor when starting up.

Is your macOS up to date?

What monitor (display) are you using?

What cable or (adapter & cable) are you using?

For a list of things to try,

go to > Get help with video issues on external displays connected to your Mac - Apple Support

I took back to the local seller, he tried on another mini with another samsung monitor, and he got the same problem. He said that HDMI seems to accept only the HDMI-HDMI connection, while the page Get help with video issues on external displays connected to your Mac - Apple Support says that I can do also an HDMI to DVI connection, through the suitable adapter. On my old i5 mini HDMI-DVI works, on my new i7 it does not work. It seems a common problem on many forums. It should be fine that Apple provides a solution.

It seems to be a common problem with Mojave.

2018 Mac Mini - monitor problems - Apple Community

Some in that discussion say the latest Mojave 10.14.6 beta (and the Catalina beta) fixes it, so if you can put up with the unplugging/plugging until the next Mojave release, you may be OK.

I have the same problem, with the same operations as Nikosiena. Contacted apple support, with negative result; the reseller service found that all his mini macs have the same behaviour. MacOS 10.14.5; monitor Samsung ColorSync 931c with DVI input; adapter Apple DVI-HDMI there is only one model. In more forums I have found the same problem (to cite the posts: "In these mini 2018, HDMI sucks" !). Maybe the problem is related to the driver for the HDMI output. I tried on my FullHD Samsung television set, cable HDMI-HDMI and works, but sometimes it looses, during start-up, its connection.

The problem is diffused, as I can see on different posts. The only actual alternative solution is to stop, but not switch-off the mini

Neither Apple support (I am in warranty and I could also contact the call center) nor this community nor the help web page did not solve. But elsewhere a guy suggested to use the USB-C connection through a suitable adapter towards the DVI-D monitor: the problem at start up disappears and everything works fine, without being obliged to buy a new monitor. The Apple HDMI-DVI adapter did not make the job, nobody knows why, and there is no technical note about the problem or how to solve it.

the correct name of the monitor is Samsung SyncMaster 931c

After Mojave 10.14.6 update the problem appears not solved. I had to buy USB-C / DVI-D connector and it works fine.