When creating new contacts, is there a way to know if a contact for this person has already been made?

When creating the contact, if the email address is already taken up for a different contact, Freshdesk would be displaying an error Email address has been taken at the top of the page. There will also be a link that would help redirect you to the contact's profile.

You can also search using the contact's email address and navigate to the Contacts section under search.