Textures are stored in files on disk, so if you see a textured mesh in Blender you need to find those texture files location in disk and use them in Unreal Engine materials. In Blender select your object and find the materials tab, or go to the “Shading” workspace (top of the viewport) and you will see the texture files there.
Notice also that when you import a fbx file in UE there is a setting to create new materials from the import or not, if the checkbox is off materials will not be imported and you will have to create new ones.