H1b 6 year maxed out -> COS to B2 is pending -> now i140 is approved. What are my options?

My h1b maxed out 3 days ago (with all recapture) while i140 was pending.
Applied COS to B2 (haven’t gotten receipt yet).
Today I got i140 approval.
My attorney suggested to file COS to H1b which means USCIS will process B2 first.
Is there any option to directly apply H1 without waiting for full process of B2? Is there no way to request an exception of some kind? I can’t travel out of US (even when borders open) as my wife is in last month of pregnancy. Am I stuck spending savings while B2 is pending?

Applying H1B COS is the right way.

I don’t know of any other option.

Thank you Anil. That’s what my company attorney suggested. Does applying for h1b cos speed up the whole process by any chance?

Every application takes its own time. I don’t know what kind of speed up you are talking about.