A couple of things I have seen that could lead to similar symptoms; Some people run the application from the disk image file, and others copy the .dmg file to Applications. Either one wouldn’t work out too well.
You download the dmg file and double-click it to mount the disk image. In there is the actual SketchUp 2019 folder, and an alias to Applications. Drag the SketchUp folder onto the Applications alias.
When it is finished copying, select “Eject SketchUp 2019 (English)” from the Finder File menu.
Go to Applications and find the SketchUp 2019 folder, and go into it. Open SketchUp. You will see its icon appear in the Dock, you could move that to another place in the Dock, or right-click on it and in Options choose to Keep in Dock. That way the icon is there even after you have quit SketchUp, and clicking it will open the right file next time.