Most of those we've filed have been turned around in 5-6 days. They usually will certify or not certify within seven working days. See 20 CFR 655.730(b).
4-7 working days is the range I've seen. Good luck on this years cap. You may be able to just get in. Too early to tell yet. Hopefully you employer is able to get things in faster next year. Normally it only takes 10 days to prepare an H-1B. Why was the LCA only filed on the March 29th? Was your lawyer behind on work? Did your employer not provide the right documentation?
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Your employer needs to retain an experienced immigration lawyer to review all the facts, advise them, and handle the case. Your employer can find one through http://www.ailalawyer.com.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.