Can I pay to speed up newborn passport?

[Pac35]

Hello!
We are booked to visit DH's family in US on 24/5/22.
We are waiting for my sons first passport, it has been 6 weeks (I know there is a 10 week wait, But we had to wait for him to be registered before we can apply for the passport). I have tried calling the passport office so many times but keep getting cut off because they're busy. According to the website, I can't book an urgent appointment to get a passport as the application is already in process. Does anyone know if there is any way to pay to speed up the process and try and get the passport in the next two weeks?
Thank you so much!

You can apply to have your application upgraded to fast track if you are travelling within 2 weeks. You need to email the upgrade team at the passport office that's dealing with the application so you'll have to call to find out which office its in (good luck getting through - I've tried over 150 times in the past 2 days). You have to provide proof of travel when you apply. You will need to pay a fee if they do ever get back to you. I wouldn't hold your breath though, I applied for an upgrade 10 days ago and have heard nothing back except an email saying they've received my request and not to contact them again. Not looking very likely we'll make our holiday in 4 days' time 😥