You can bypass the login page for RStudio Server Pro by using proxied auth, but not when using LDAP/AD. In that case you would integrate the underlying Linux server with the AD domain, c.f. https://docs.rstudio.com/rsp/configuration/authentication/active-directory/, and typ in your username and password at the login page.
BTW, one advantage of the LDAP/AD integration is user provisioning. With proxied auth you have to make sure the required users exist on the Linux system. With the LDAP/AD server integrated into PAM, the user creation can be automated.