Connecting to Cisco AnyConnect VPN without stored certificate or shared secret
I believe that the AnyConnect client can be used to connect to a number of different types of VPN offered by Cisco.  The process you describe above leads me to believe that you are connecting to an SSL-VPN. SSL-VPN does not require the use of a shared secret for the first layer of encryption.  Instead the client and the server auto-negotiate that first layer encryption using SSL.  You are then asked for credentials and a group membership.  The remainder of your VPN session is uniquely encrypted following Authentication.

You could script the connection so that instead of having to enter your credentials each time, you can store them in your keychain, and simply initiate the connection from the shell, or other script.  I did so a few years ago here:  http://www.wellingtonnet.net/code/2014-02-04/cisco_anyconnect_client_mac.html

I have noticed that with each update of AnyConnect, I have had to tweak this script, so use it as an example and go from there.  It has been about a year since I last needed to connect via AnyConnect.