How can I work out who created an Azure resource, older than 90 days old?

You can't. The only way to keep logs for longer than 90 days is to archive them to a storage account

https://docs.microsoft.com/en-us/azure/monitoring-and-diagnostics/monitoring-overview-activity-logs#export-the-activity-log-with-log-profiles

or integrate it with Log Analytics

https://docs.microsoft.com/en-us/azure/log-analytics/log-analytics-activity

If you don't have any of those configured, then there's no way to tell.

I agree with Bruno Faria. On Azure Portal, you could find when the resource is created. Maybe this will help you find you want.