Talk to your immigration attorney. There is a presumption of fraud when you get married within the first 30 days of entry. The presumption is still there in the next 30 days, but burden of proof changes. If you wait at least 60, there is no presumption, although it can still be argued. You really need to talk with your attorney, going through all the facts.
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Do what the lawyer you hire advises. BTW, once the adjustment of status application is filed you are allowed to legally remain in the U.S. and do not accrue unlawful status until the application is adjudicated.
Certified Immigration Law Specialist*
Law Offices of Tasoff and Tasoff
16255 Ventura Blvd. Suite 1000
Encino, California 91436
I respectfully disagree that filing an adjustment of status application makes your stay here safe. VWP entrants have different rules than everyone else, and an administrative removal order can still be entered against you after your adjustment application is pending. An if that happens, your adjustment will be denied. You're playing a risky game, and I suggest you keep meeting with attorneys until you find someone who makes you 100% confident in his or her advice (which you don't seem to be yet).
Also, NOA1 is not a real thing. My guess is that you've picked up that terminology from something like visajourney.com and have been led to believe its a real legal name. It's not. It's the filing receipt, and calling it that will help attorneys better understand what you're talking about.
THIS ANSWER IS FOR INFORMATIONAL PURPOSES ONLY, DOES NOT CONSTITUTE LEGAL ADVICE, AND DOES NOT CREATE AN ATTORNEY-CLIENT RELATIONSHIP. Immigration is complicated and the wrong action can have serious consequences. Never take action in your case based solely on general information like is offered here. Speak to an attorney who can give you specific advice about your own situation.