So that photo is your template and you want that as a vector artwork?
You can use Image Trace. Trace that in black and white.
Expand.
Delete everything that is not your artwork.
Then apply whatever color you need.
Here is a video: https://youtu.be/315XXc4th4Q
Bildnachzeichner = Image Trace
Umwandeln = Expand
Ebenen = Layers
You will have to discuss with the printer, exactly how they want that artwork delivered. It depends on several factors.
Make sure you respect copyright when using that image. Maybe it's yours or you have aquired the necessary rights, but maybe not.