We have a distribution group and email@example.com mail addresses in it. I add mine real mail address to members section. When someone sent e-mail to firstname.lastname@example.org i receive mails. There is no problem.
But i need reach some old mail in this email@example.com mailbox. Because i am a new member of this group. But i can't find the firstname.lastname@example.org in Mailboxes section in Exchange Admin Center for reseting the password.
Distribution groups do not have a mailbox and there's no way to access older messages sent to the DG. If you mean you're using a Microsoft 365 Group, you can access it via Outlook/OWA, as long as you are a member of the group. In the EAC, the corresponding object will be found under the Recipients > Groups section.