Hello! Yes, this is possible, but the other person needs a familyecho.com account to do so as well.
To share the tree, select a (living) person on the tree and then click on the "Share" button on the bottom of your screen. Now choose "Edit family" under "Permissions" on the top of the sidebar and then either use the built-in option to directly send an invite link per E-Mail or choose "Create link" below (and of course copy the link and send it to your family member).
Without a familyecho.com account, your family member can view the tree and edit the person you clicked on while sharing the tree (i. e. if you clicked on "Aunt Thelma" and then on "Share", they could only edit Aunt Thelma). To add new people and correct the information of other people, they need an account themselves.
Hope this helps!