Last tested: May 2020
SQL Runner only shows the first 500 tables that the Looker database user has permission to within a schema, and it doesn't update very frequently.
First click the gear on the left hand side and select "Refresh Schemas and Tables".
If that doesn't work, try a simple
SELECT * FROM desired_table LIMIT 10. If the table is there, then Looker might just need some time to see the table and update the list.
Otherwise, you might get an error giving you more info about the existence of that table and your permissions to it. It's possible that you lack permission to that table, or that you lack sufficient permissions to the databases' internal schema. (These are all database-level permissions that the Looker database user needs.)
This content is subject to limited support.