Before entering any negotiation you should first know what is your goal, once that's decided, you decide the minimun that you'd settle for. If the only variable that you're considering is money, then that's easy since you probably already know the value of your work in the market. If not, your reasons for accepting the offer become personal (work culture, position, personal goals, etc) and we can't really help you decide. And since that's your dream company, should you really be considering only salary? Is it really your dream company then?
I assume you passed a long selection process and is not common for an entering employee in this situation to negotiate after an offer has already been made, it can happen and is acceptable, but uncommon. Therefore, if I would like to renegotiate the salary, I would ask for a meeting and present my terms on why I should receive more but also be prepared to receive a "no". Since I never generated value to them, there are other people ready to take the position and they have no real reason to raise the offer.
But, if you never participated in any selection and it's them who are after you, then you should totally negotiate on your own terms and an email is more acceptable. I would write something like:
I am interested in the position you're offering, but the salary is not exactly what I expected, are you able to offer a value closer to $X? If you have an avaible time in your schedule we could talk better about this.
Finally, the best I can recommend to help with your imposter syndrome is to seek professional psychological help if you feel like it difficults your personal and professional life.