No DORICO icon to open it when I have everything installed

If you find and open Steinberg Download assistant, it should look like this (on the right) where it is showing my Dorico has been installed (green, and if I want to install it again).

If there is no green, it should say to install.
This only works if you have redeemed your activation code (see Redeem Code top left), which is what you receive after purchase with an email.

Otherwise as @k_b has said, we really need more information from you, otherwise we are guessing.