Yes, you are right, You need to have Microsoft Certified: Azure Administrator Associate (AZ-104) and then complete the Designing Microsoft Azure Infrastructure (AZ-305).
Once you complete the pre-requisite, you will get the certificate and the badge automatically.
Also, can you suggest to me preparation material?
https://learn.microsoft.com/en-us/certifications/azure-solutions-architect/ - Modules here are enough to pass the exam.
As an average, how long takes the preparation time?
I would say it takes somewhere around 3-4 weeks