If you are not receiving email Notifications to Google's Smtp service then one of the issues involved may be that you are not using TLS.
Once you've enable this your Mail notifications should be received at a faster rate. Be sure to check you do not exceed your limits per googles SMTP and Mail relay rules.
To verify the issue you may download the TSR report and review the mail log files to see if you have any messages that says:
Nov 24 16:14:32 neupbx sendmail[9352]: sAN07BbQ028373: to=<support@goneutrino.com>, delay=2+00:07:21, xdelay=00:00:00, mailer=esmtp, pri=5694471, relay=goneutrino.com.inbound15.mxlogicmx.net., dsn=4.0.0, stat=Deferred: Connection refused by goneutrino.com.inbound15.mxlogicmx.net.
Here is addtional information as to why your message may have been deferred by google.
https://support.google.com/a/answer/2956491?hl=en
Affected Version(s)
SMB 5.9;SMB 5.8