Trigger the Start Process at the moment of SAML Authentication

That is not supported. What are you trying to do?

If you want to know that a User has logged in there's the login-audit.cvs file in the logs you can refer to. If it's something different please elaborate.

I want to control which user is created on Appian, not all user that exist in IDP has role to access application in Appian. Therefore, IDP response success but if I check the roles, there will be no role in Appian for them, therefore I do not want to create that user automatically. Same for group, I do not want to create group automatically without a validation for my side. 

Why don't you control the management of Users/Roles in Appian using some LDAP Synch (or equivalent), and keep the authentication aspect (SAML) separate? That is: treat them as two separate problems. I assume you'd want to deactivate users who have bene deactivated in your IDP, and change their roles as they change in the IDP...so implement something that manages user accounts in Appian and use SAML purely for authentication purposes. 

This is so confusing. Can you help clarify, give context and share details?

Yes, it is possible to trigger a process or apply logic when authentication with SAML is successful. SAML is a standard for exchanging authentication and authorization data between parties, typically between an identity provider (IdP) and a service provider (SP). Once a user successfully authenticates through SAML, the service provider can access the user's information from the SAML assertion and use it to trigger processes or apply custom logic.

Thanks, this approach works for me, according to this I will build a process to management of Users/Role at a different time than the authentication with SAML