There is no real world flat surface which goes on forever. It is a geometric idealised concept. So, since there is not even a first such thing, there cannot be another.
A flat surface that extends forever is a plane
A plane.
Plane
Plane
lever
A flat surface that extends forever is a plane
A plane.
A plane
A plane
A plane
Plane
Plane
A plane.
a plane
lever
A floor.
A solid figure that has a flat surface that is a circle is a cylinder. A cylinder consists of two circular bases connected by a curved surface. The flat circular surfaces are at the top and bottom of the cylinder. Another example is a sphere, which has a circular cross-section but is not flat overall.