Welcome to ODK Forum, if you have a moment, feel free to introduce yourself here.
Currently there is no public access link to edit submissions. However, if you create a hyperlink pointing to the submission edit (eg: https://yourdomain/v1/projects/1/forms/simple-form/submissions/{submission-uuid}/edit) and user is already logged in the Central in any browser tab/window then they will not see the login. Additionally, if users are expected to edit multiple submissions then at worst they will see login only once.
ODK Central also support Single Sign-on (SSO), you can configured that, then users won't be required to log in when they link on edit submission link on your dashboard, assuming users on the dashboard are authenticated with the same OIDC provider.