Put picture from imported pic as vertex paint and engrave / extrude the shape from other object

You have to convert it to .SVG, then import it as SVG. It will be much better if you remove the white background let it transparent.

You can use online converter but make sure it encodes the image to svg, simple conversion can't be imported into Blender.

It will be imported as curve convert it to mesh using Alt + C

Usually this is how I do it....

Convert the Jpg or Png into SVG format. You can find a
free online converter on google search. Keyword to search
is "Converter Jpeg to SVG" or "Converter Png to SVG".

You can then import the SVG format as a spline. With the
spline, you could then convert it to mesh. Fill those faces
and extrude those faces.

To cut the words into a cube, you would use the boolean or
booltool ( An easier and a better way to work) in Blender
to accomplish the task.

NOTE:

You may have to watch a few topics on youtube on the subject
I have pointed you to. Else there will be too much instruction
to write up.