SAML based SSO with Laravel
'sp' => array(
'x509cert' => 'I ADDED x509certs here which I downloaded from google','privateKey' => '',
You are using Google as IdP so, why are you using google public cert on the sp section?
If you plan to sign the SAML messages sent by the SP, then you need to place there your own cert/private key. You can generate self-signed certificates with this tool: https://www.samltool.com/self_signed_certs.php
If you have doubts about some settings fields, review the documentation of the Lavarel SAML plugin, but also review the documentation of php-saml, the SAML toolkit that the plugin uses.
In order to debug what is happening, I also recommend you to use a browser extension to record your SAML Messages, use for example SAML Tracerand review the Status of the responses that will inform you about a possible error.