yes, but it seems that you anyway need a visa run, unless you find a job before you enter taiwan.
you need to apply for resident visa 8 work days before the expiration date of your current visa with a work permit obtained by your employer. Processing time for the work permit is 7 working days. If you look for an employer after you come to Taiwan, you need at least 15 work days. even if you find an employer and they apply for your work permit on the day of your arrival, you cannot do that with your tourist visa for 14 days.
Resident Visas for White Collar Workers
https://www.boca.gov.tw/cp-166-276-48430-2.html
The number of days for review ( for work permit)
https://ezworktaiwan.wda.gov.tw/en/cp.aspx?n=5C02376F2E8E8DBB
basically you need a degree and 2 year experience relevant to the job. You will find details on work permit here.
Workforce Development Agency/EZ Work Taiwan
Home/Foreign Professionals to Work in Taiwan/ Specialized or Technical Works