Job offer's salary is a lot lower than advertised/discussed

I recently received an entry-level offer at a specialized engineering firm after my graduation this Spring. The starting pay is roughly 15-20% lower than the bottom of the range they had advertised in the job posting.

I also have a pre-planned 3-week trip home about two months after the start date. Is it risky to negotiate a higher salary while also asking for unpaid leave for a trip this early? I don't have a backup offer yet and I'm worried about the offer being rescinded. Has anyone successfully navigated this? Thank you beforehand.