I am wondering if this negation [沒有] by itself expresses a past tense or a completed action . So can we say 我没有去上班 without adding any adverb and understand I didn't go to work. If so can 有 be omitted ?
Yes it can. To me, the 有 is more like an emphasis.
I think the two negations 不 and 沒 both carries tenses on their own when negating action verbs:
沒 - have not start/been completed something.
不 - do not, can not, may not, will not do something. Also in conditionals.