Please fill out the fields below so we can help you better. Note: you must provide your domain name to get help. Domain names for issued certificates are all made public in Certificate Transparency logs (e.g. crt.sh | example.com), so withholding your domain name here does not increase secrecy, but only makes it harder for us to provide help.
My domain is:msagresidents.org
I ran this command:N/A
It produced this output:N/A
My web server is (include version): Google Workspace
The operating system my web server runs on is (include version):Unknown
My hosting provider, if applicable, is: Google
I can login to a root shell on my machine (yes or no, or I don't know):I don't know
I'm using a control panel to manage my site (no, or provide the name and version of the control panel):Google Workspace Admin
The version of my client is (e.g. output of certbot --version or certbot-auto --version if you're using Certbot):N/A
Thus you need to own and have control over the Domain Name (or have a subdomain under an existing domain name, for example pointed to your server by your employer or school) you wish to obtain a certificate for, from an ICANN Accredited Registrar.
In the title you state non-public domain, Let's Encrypt does not offer certificates of that type.
Here is a link Create Local SSL
The only page that is public is a landing page that then takes the user to a login screen where they enter their Google Workspace credentials for accessing the (internal) Google Sites website. Once there, they can access the Google Workspace apps like mail.google.com and calendar.google.com with their logged in credentials. I think we need the SSL certificate for the landing page only.
Somehow Turbify became our DNS nameserver and when some users put in 'msagresidents.org' in their address bar, they get a Site under construction message from Turbify. Most of the time they can just reload and it will take them to the right page, but it's annoying.
Your DNS for your apex name is using Turbify's service. Can't you just set the A record to be the same IP as your www subdomain? And then ask google workspace to grant a cert for both names?
Your DNS
msagresidents.org. 120 IN A 35.168.67.138
msagresidents.org. 120 IN A 3.230.199.117
www.msagresidents.org. 1200 IN A 216.239.34.21