Hey there! I can confirm that you would not be able to access your invoice if you downgrade the plan (here with a Starter plan). In the future, if you upgrade and downgrade again, I would advise you to download the invoices before downgrading. 

Here is an help article with the recommendations regarding that:
https://help.figma.com/hc/en-us/articles/360039829734-Cancel-or-downgrade-Professional-plan

In the meantime, I’ve submitted a support ticket for you (your ticket number is 1228728). Please specify in the support ticket the period for which you need access to the invoice so that the support team can assist you further. Thank you!