Let's say, while you're on vacation (within the 3-month limit for tourist stay), that you got a job offer from a Japanese company. Is it possible to have your tourist visa converted to a work visa without leaving Japan?
It is not possible to “convert” travel visa you have, but you are able to look for a job that provides visa sponsorship.
Once employer agrees to hire you, you or they will have to apply for Certificate of Eligibility. Having that issued you can get a work visa, change your immigrant status and be hired.
The whole process takes much time (several months), which would probably exceed the time allowed by travel visa. It is not problem because most important thing is to get hired, then it's just a paper work and waiting time.
You could also look for a job remotely, but if you think there're more chances to get hired when you're onsite, then consider getting study visa first (e.x. Japanese language schools), which allows you to be in Japan for 3 to 12 months or even more.