Vinyl siding can be removed. It's usually only nailed to the underlying sheathing of your home. For a brick facade, I am aware to two methods:

A mason will need to create a "brick wall" that runs close and parallel with your home's front sheathing and is "tied" to house. Of course, this brick wall will need a firm foundation.

Another method is "brick-face". The vinyl is removed and wire mesh is installed onto the home's front sheathing. Then the mesh is imbedded in a layer of mortar and thin "bricks" are applied or in some cases a layer of tinted mortar that is later scored reveal the untinted mortar, to look like individual bricks.