A lot of times when a doctors office makes an appointment for many months away they will tell you that either they will call you if a time slot opens up sooner or they will tell you to call them occasionally to see if they have a sooner appointment. So you might want to call and talk to them and maybe they’ll call you up if someone cancels and you can be seen quicker.
This happened to me with the sleep clinic for my sleep study. I called in March for an appointment and they made me an appointment for December but they called me a month and half later and gave me an appointment in August.
My hospital has an app I can use for all interactions with those doctors in that network. They have a button you can click to be put on a cancellation list. They will email me if there are any openings. I just have to pay attention before the offer expires and they contact someone else.