Contact forum not sending Email

Hi, I’ve been setting up my site and the quick contact forums arn’t working. The only one that seems to work is the email at the top of the page will open a template in my Inbox for me to send the mail manualy. But the quick contact and contact forum seem to work from a clients point of view, saying the message has been sent but does not come through.

I’ve looked around the forums and only seen similar resolved issues with private replys.
Quick note, I’m trying to have the Email go to a custom Email made with G-Suite. So I think it mayswell be a Gmail?