Where can a system administrator assign a page layout in Salesforce?

Hi Anuj,
The answer to your question is Profile and Record Type.
You can refer to the following trailheads in order to clear your doubts.
Ref: https://trailhead.salesforce.com/en/content/learn/modules/lex_customization/lex_customization_page_layouts
https://trailhead.salesforce.com/en/modules/lex_migration_customization/units/lex_migration_customization_layouts_ui
And this: https://help.salesforce.com/articleView?id=customize_layout.htm
Hope this helped !