Hi Youngjun- Julianne from Mixpanel Support here!
I hate to be the bearer of bad news, but it isn't possible to work around the ID Merge delay if your Funnel is analyzing pre and post-login events. If you're troubleshooting a specific user, the Users page shows the merged events streams immediately. However, reports like the Funnel will have the delay. Apologies for not having better news there.
Most merges usually happen within a few hours, so if you are looking at data from today, you could add a delay of a few hours to the report to generally be analyzing merged data. I wouldn't recommend identifying anonymous users though since that isn't expected with ID management.