Thanks for reaching out. The other possible options could be selecting the objects from the layers panel and you can also try expanding the layer panel. You can also refer to this help article for more information: https://helpx.adobe.com/xd/help/layers.html
Let us know if this helps or if you need any further assistance.
Thanks for the tip. While this in deed helps with selecting the icon, it does not help with placing it. I can use arrow keys for small distances, but if I need to move it further away, I need to click&drag in the design.