Most people who become sick and get mesothelioma from exposure to asbestos have been working around asbestos for many years and sometimes as long as 20 to 30 years before the asbestos exposure causes the mesothelioma.
Still being exposed to even a little bit of asbestos is not good and could cause mesothelioma after many years.
So avoid touching or disturbing asbestos if possible just to be safe.