Creating a pyramid from scratch using the Bmesh Blender Python module. (video tutorial here: https://youtu.be/N3U2noAHgBo)

create_shape_from_scratch_with_bmesh.py

import bpy
import bmesh

obj_name = "my_shape"

# create the mesh data
mesh_data = bpy.data.meshes.new(f"{obj_name}_data")

# create the mesh object using the mesh data
mesh_obj = bpy.data.objects.new(obj_name, mesh_data)

# add the mesh object into the scene
bpy.context.scene.collection.objects.link(mesh_obj)

# create a new bmesh
bm = bmesh.new()

# create a list of vertex coordinates
vert_coords = [
    (1.0, 1.0, 0.0),
    (1.0, -1.0, 0.0),
    (-1.0, -1.0, 0.0),
    (-1.0, 1.0, 0.0),
    (0.0, 0.0, 1.0),
]

# create and add a vertices
for coord in vert_coords:
    bm.verts.new(coord)

# create a list of vertex indices that are part of a given face
face_vert_indices = [
    (0, 1, 2, 3),
    (4, 1, 0),
    (4, 2, 1),
    (4, 3, 2),
    (4, 0, 3),
]

bm.verts.ensure_lookup_table()

for vert_indices in face_vert_indices:
    bm.faces.new([bm.verts[index] for index in vert_indices])

# writes the bmesh data into the mesh data
bm.to_mesh(mesh_data)

# [Optional] update the mesh data (helps with redrawing the mesh in the viewport)
mesh_data.update()

# clean up/free memory that was allocated for the bmesh
bm.free()