embroider the bottom contact point
Layer with filler material. Make some holes in the material to enable the conductive sides to touch when pressed.
Layer with conductive fabric in a way that it does not overlap with the place where the bottom contact point connection.
Place any fabric on top to insulate the conductive fabric. Cut away all the extra fabrics around the edge of the button.
Embroider a thicker edge for the button- I used Satin stitch.
Peel away the rest of the filler material.
Embroidered push button with two connection points.
Testing with a multimeter
The two conductive parts connect when button is pushed.