User default roles for new user creating a new subsite

I have a wordpress network. I want to control the menu items they see, including the ones created by plugins so they have limited control.

(I am controlling the updates, addons, certain settings, etc.)

How can I make sure that when a user creates a new subsite on my network that they cannot see the menu items I have chosen to hide from them on the dashboard?

I used advanced access manager to create a custom role that gives the permissions I want to give to users WHEN THEY CREATE A SUBSITE. However, I cannot make this custom defined role the default role for the users who create a subsite for their subsite. Is there any way I can make a default role my custom defined role?

If not, is there a way I can hide all the menu items I do not want admins to see when they create a subsite, without affecting my super admin privileges?