Hi esteinberg1,
We appreciate you reaching out to us. We understand that you are experiencing issues setting up your Time Machine backup, because you are getting a "Not enough disk space" message.
We’d like to gather additional details that may help us be in a better position to assist you.
Have you had the chance to try a different external drive?
Are you using the same steps in the article below to set up your Time Machine backup?
Back up your Mac with Time Machine
I the meantime, we recommend that you check if the issue persists when signed in on a different user account.
The article below can help if you do not have any other user account to test with.
Set up users, guests, and groups on Mac
If you are experiencing the issue when signed in on a different user account, we recommend that you check if the issue persists while on safe mode.
Below is an article to help guide you through the process.
How to use safe mode on your Mac
Take care!