If you cannot apply for TARC through your parents, you have to wait in line just like everyone else.
Companies do not sponsor TARCs, they can’t. They can only apply for your work permit which leads to regular ARCs, anything else has to be done on your own.
this is misleading. Companies don’t sponsor TARCs is right. They apply for OP’s work permit, which leads to regular ARC or TARC. Whether they do the procedure to apply for ARC or TARC for their employees is up to them. saying ARC or TARC based on employment is sponsored by company may not be so wrong.
By the current immigration act, employment based TARC holders should stay for 3 years to get a hukou. But there is a draft to amend immigration act. if it is passed with no change, the shortest duration would be a year with more than 335 days in Taiwan.