When I click on the new button on Lead object (which is a standard button) page.
It opens a standard Standard page.
How to make a field mandatory on a standard page? Is there any other way apart from a Validation Rule?
You can't make the Standard Address field mandatory on the the field or the page layout. There is an idea in place for this, though the last comment from Salesforce is that this it not on the current roadmap
https://trailblazer.salesforce.com/ideaView?id=08730000000BqlNAAS