MySQL can take more than an hour to start

I have a mysql (Percona) 5.7 instance with over 1Million tables. When I start the database, it can take more than an hour to start. Errorlog doesn't show anything, but when I trace mysqld_safe, I found out that MySQL is getting a stat on every file in the DB. Any idea why this may happen? Also, please no suggestion to fix my schema, this is a blackbox. Also keep in mind that I've heard it all regarding how bad the design is.... Thanks