Can I avoid a DUI conviction if I was charged after crashing into a road closure sign that was unsafe (violate DOT guidelines) to begin with?

It will depend on what your blood-alcohol reading was. The fact that you had 2-3 beers is not enough facts to really analyze your situation. I strongly suggest that you contact an experienced criminal defense attorney for a face-to-face consultation and give him/her all of the facts surrounding your arrest. He/she would then be in a better position to analyze you case and advise you of your options.

The mere fact that the sign wasn't posted properly will not automatically shield you from a DUI charge or conviction. But, it is one factor a good attorney might be able to use to help defend you. Consult an attorney immediately.

Can you? Sure. Is it likely? No. You admitted to driving, and to drinking. However, I can help you fight the criminal charges and get the best outcome possible. When arrested or charged with any crime, the proper questions are, can any evidence obtained in a test, search or confession be used against you, can you be convicted, and what can you do? Raise all appropriate defenses with whatever witnesses, evidence and sympathies are available for legal arguments, for evidence suppression or other motions, or for trial. Effective plea-bargaining, using those defenses, could possibly reduce the potential time and other penalties you face. While this isn't a 'capital case', you certainly face potential jail and fines, so handle it right. If you don't know how to represent yourself effectively against an experienced prosecutor intending to convict, then hire an attorney who does, who will try to get a dismissal, charge reduction, diversion, program, or other decent outcome through plea bargain, or take it to trial if appropriate. A little free advice: When arrested for DUI, whether alcohol or drugs, then upon release from jail or booking the defendant is given documents that include a notice that you have only ten days to file a request with DMV for a hearing on an appeal of an automatic one year suspension of your license imposed by DMV. That is separate and runs consecutively with any suspension that may be imposed by the court. Contact DMV and do so, timely, then appear at your scheduled DMV appeal hearing and present any supporting evidence and testimony. If you don't know how to do these things effectively, then hire an attorney that does.

You need to hire a DUI specialist. You have a good case, because no one saw you driving, so the cop can't describe the manner you drove and the time you drove. But without a good DUI lawyer you're still left with no choice but a guilty plea.

You seem to be asking if the fact that the officer did not see you driving, and/or that the sign was illegal, are defenses that would allow you to avoid the charges. The answer is NO. You admitted to driving, the accident allows he officer to make the arrest. Other defenses are available but were not specified in your question.