Microsoft SQL Server - Permission to create a Snapshot
Its not possible to do straight away as mentioned on MS documentation:


  Permissions Any user who can create a database can create a database
  snapshot; however, to create a snapshot of a mirror database, you must
  be a member of the sysadmin fixed server role.


What I understand is - if you could have alternative in place for DB creator role, this purpose can be achieved and this has been explained very well by one of MSSQL SME Mr. Solomon Rutzky

You can achieve this by using module signing which has been explained by Mr. Tibor Nagy on this link --> https://www.mssqltips.com/sqlservertip/3336/how-to-use-module-signing-for-sql-server-security/

You can also refer the question and answer thread for better understanding of module signing at the same forum and how can this be used:

Granting a user a permission to restore a database

Execute Permissions for a Store Procedure that creates databases

https://sqlquantumleap.com/2018/02/15/safely-and-easily-use-high-level-permissions-without-granting-them-to-anyone-server-level/

More about Module signing at Microsoft:

https://docs.microsoft.com/en-us/previous-versions/sql/sql-server-2008/ms345102(v=sql.100)

Hope this leads you into right direction.