In order to connect to a SharePoint site with an email account external to the domain hosting the site, you will need to follow these steps.
In your email client, locate the Welcome Email for the new SharePoint site and open it.

Click on the Link provided for the new site.

Use the email account you have used for the group to sign in with.

If this email account is an existing Microsoft email account, go ahead and use your current password for that email.
If this email account is NOT an existing Microsoft email account, if you are presented with a password, click the link to send a code, otherwise, Microsoft should send a one time code to the email address you are using.

Once you receive the code, enter it in the space provided.
In both cases, once you have logged in successfully, you will be asked to accept the Permissions for the site.

click the Accept button to continue.

Click the Next button to continue to setup up 2FA/MFA for the site.

If you already have Microsoft Authenticator setup on your mobile device, go ahead and use it. If you have another MFA app setup like LastPass, click the I want to use a different authenticator app link and set it up using that wizard. As a refresher, you can use the link for https://wiki.computersdotcalm.com/doku.php?id=microsoft:add-lastpass-mfa on this site on how to do that. If you have neither setup, click the link for I want to set up a different method at the bottom of the form to use your cell phone for authentication.

If you will be using just your cell phone for the authentication instead of a MFA app, once you click the I want to set up a different method link, you will be asked what method to use.

Change the drop down to Phone and then click the Confirm button to continue.

Enter in your phone number in the space provided and then click the Next button to continue.

Once you receive the code on your phone, go ahead and enter it in the space provided and the click the Next button to authenticate.

When successful, click the Next button to continue.

Click the Done button to continue to the SharePoint site.