How to start navigation from the mobile phone?

Never tried it but SendPoints may do what you want.  It's a Garmin IQ app.   https://apps.garmin.com/en-US/apps/93712e86-cec9-48c3-b18e-2a87aefead91#0 

May be others.  I'm assuming you are after a single waypoint not a course.

Thank you, this looks good. I would prefer something without third-party service, but sendpoints also works for me.

you can sync/add/modify waypoints with basecamp from computer. Also play with Garmin Explore and Earthmate - both Garmin mobile apps.  They are not always intuitive to use but can sync to devices.  Again, I have not specifically used them for waypoints. 

Just tried Garmin Explore on my phone. Added a new waypoint, added that to my Fenix 5x collection and synced.  It was then available to Navigate to a saved location from the watch. 

I am looking more for a app when I am somewhere and know a location on a smartphone app like google maps and want to start navigating to it.

Looking for points of interest works when you find it in the list. Navigating the (watch) map is not so convenient and you need to know where on the map the POI is. And the search using a sector doesn't work for me or I did not understand how to use it.

So in the end I would like to have some map point (google maps, osm, maybe a location received by an instant messenger) and send it to the device to start navigating.

I tested sendpoints from the PC and it works and I assume it works on the mobile in a similar manner. The drawback is that it will only work when you're online otherwise it is quite useful.

I tried explore and it did not connect to my watch (garmin fenix 5+) and I thought it may not be compatible. When it works with your 5x I'll try again.

I think it is more a case of connecting to your Garmin account and then adding in the watch from your list of devices.  As I said earlier the Explore side is not all that intuitive but does work. I don’t use it enough to be a great help with it - sorry. All I can say is I did just pass a waypoint to the watch!!