Much depends if you wanted a "calendar year" or a "fiscal year". I am not sure your question required a month but rather a year. You will want a CPA on a go-forward basis anyway, and this would be a good first question.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
The instructions to form 2553 state that A corporation making the election for its first tax year should enter (a) the date of incorporation, (b) the date the corporation first had assets, or (c) the date the corporation began business.
Hope this helps.
Phillip M. Smith Jr.
Los Angeles Tax & Business Attorney
Licensed in the United States Tax Court
Main: 323-292-4116 ❘ Cell: 562-505-1004
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Mr. Smith gave you the correct answer in terms of the dates you can select: (a) the date of incorporation, (b) the date the corporation first had assets, or (c) the date the corporation began business. You can't select January 1 of 2013 since it didn't exist on January 1 of 2013. So whether you pick May 1 or June 1 sounds fine.