There are several ways to achieve this. If you want to use a dropdown, you could add a button next to it. If the address can’t be found in the dropdown, the user can click the button. This button would call a microflow that creates the address object, associates it with your other object and opens the Address_NewEdit page in which the user can enter the details. Clicking save will now store it to the database and it will already be associated with your main object (because the microflow already did).