Oracle - how to find what caused CPU to spike 3 weeks ago
If you have your AWR settings were set up to retention other than default 8 days, for example 30 days, then answer is yes. Or if you have backup of database of that time.

Check settings by script:

SQL> @?/rdbms/admin/awrinfo.sql

At the start of output check for row:
"Snapshot interval is 60 minutes and Retention is 30 days"

If AWR retention is enough and if you have license on Oracle Diagnostic Pack then you can run ashrpt script to see the approximate load on this interval.

SQL> @?/rdbms/admin/ashrpt.sql