It will not change the meaning of the sentence if you omit “的". However, the sentence is not complete without the word "的".

i can understand it even if u (or others) omit “的” i am a Chinese. it doesnt matter in dairy life if people say it without 的 some grammer Nazi care it.

for example, 这个人是（被）你杀的。 it is you who killed that person.

是......的。 means it is ... that ... we highlight the part which is between 是 and 的 as we highlight the part which is between it is and that

You can't omit ‘的’ because of the presence of ‘是’. If you omit it, the sentence will not be grammatical. "...是...的" means "It is that...". So "他是去年六月开始在这里工作的" means "It is since June of last year that he has been working here." By contrast, "他去年六月开始在这里工作." means "He has been working here since June of last year." Obviously, "他是去年六月开始在这里工作的" is only said to someone who has already known that 'he' is currently working here. What the listener doesn't know is the time when 'he' began to work here.