Welcome to the Airtable community!
You cannot access Airtable data without an Airtable account, unless the data still exists in someone else’s Airtable account and there is a public share.
You can archive your data by exporting it to CSV files.
You can also try downgrading to a free account. If your base is over the record or attachment limits, you will get overage warnings. However, in my experience, the data is still readable.