Is there any way to facilitate my taxes to get processed in Oregon? I stupidly e-filed via Turbo tax on 3/25/24 and now have to wait until August for my refund. Help!!

E-filed 3/25/24, in May, OR state requested I mail W-2 forms to prove withholding.  Done 5/3/24. Website says 12 weeks or more to process.  I WISH I had just mailed in forms!  E-filing was a total fail.  Looking for anything I can do to help this process.