Can you change the shipping address for your government issued ID

Long story short, I’m moving states and currently have no proof of address for where I currently live. I will be going back to my original state to pick up important documents because currently I will not be able to show proof of address for where I currently live. However, I do not want to be in the state I am from waiting for the ID to ship in the mail at that location. Is there a possibility for me to get my ID picture and stuff done in my original state then to get it shipped to where I live currently? Also, I am currently living under someone else’s name with no bills. I also do not currently have a debit/credit card or a job. I need my ID to obtain anything and I do not have any of that. Any advice?