An "Offense" with reference to "First Offense," "Second Offense," etc generally refers to being convicted of an offense. Have you been convicted of a crime? If not, then you do not have a First Offense. If the police search your computer, find nothing, and give it back to you, you do not have a First Offense.
Now that I have said that, your question bothers me a little (or a lot). You sound like you are trying to find out if you can look at child pornography and if caught, would it be your first or second offense? If that is the case, go get help and never, NEVER, do such a thing!
The comments listed here do not create an attorney-client relationship. The comments are for informational purposes only and are not to be considered legal advice. This attorney is only licensed in Michigan and does not give legal advice in any other state. All comments are to be considered conversational information and you should not rely on these comments as legal advice or in place of retaining an attorney of our own. The comments here are based solely on what you have provided and therefore are general in nature and with more specific facts or details a different answer or outcome could result. The legal system is not a perfect science and this attorney does not guarantee any outcome.
I agree wholeheartedly with the first answer, in particular the last comment. If you are concerned about what might happen with a 'second offense,' even though you escaped having a 'first offense,' I suspect you are an offense waiting to happen. Get whatever help you might need to avoid that happening.
Although I am an experienced CA criminal defense and appeals attorney, I can not 'guarantee' that my answer is entirely accurate, since I have not reviewed all of the factual circumstances of the case, nor have I discussed those circumstances fully with the questioner. The fact that I have answered this question does not establish an attorney client relationship between the questioner and my self or my office.
To drive the point home, a link below is provided to the Gourde case, 9th circuit. It means you should consider every site as a sting site and never join any site, and do not download anything on your computer. The predecessor case held for suppression and the later rehearing of the same case for "no suppression". Avoid temptation to do illegal things.
Curt Harrington Patent & Tax Law Attorney Certified Tax Specialist by the California Board of Legal Specialization PATENTAX.COM This communication is general information and not legal advice, and does not create an attorney-client relationship. This communication should not be relied upon as any type of legal advice. Please note that no attorney-client relationship exists between the sender and the recipient of this message in the absence of either (1) a signed fee contract and (2) remission of an agreed-upon retainer. Absent such an agreement and retainer, I am not engaged by you as an attorney, nor is any other member of my law firm.