Unfortunately, there's a saying that you may have heard which is "Ignorance of the law is no excuse." Everybody here is deemed to know all of the laws of the land,even though, of course, we really don't. So while your being a first time applicant is an explanation for what you did, it doesn't rise to the level of a criminal
defense to the charges.
You will be expected to pay back the government for their overpayment. If Welfare believes that what you did looks like deliberate fraud to them, they will turn the file over to the DA's Office for prosecution. The charge is a felony, however, if you have no previous contact with the criminal justice
system and wanted to dispose of this case, it usually results in felony probation (five years) and restitution to the government. While this can give you a record and while the sentencing laws would allow for prison on a case like this, if you make all of your court dates responsibly, jail should not be something you will have to worry about.
You will need a lawyer, and if you can't afford one, when you show up in court for your arraignment, if this matter gets that far, you would simply plead not guilty to the charges, tell the judge that you do not have the means to get yourself representation and ask him to appoint you a public defender.
Once you have your lawyer, he can go over the case with you and confer with the DA and negotiate an offer if you want one, or move the case towards trial
if you don't. But even if you want to take a plea, remember that on your arraignment (first court date) when the court asks you how you uplead, it must be NOT GUILTY). That is the only possible plea to take if you want to keep all of your rights. You can always change that plea to guilty after a lawyer has explained everything you need to know, if there's a nice deal from the DA you want to take. But it doesn't work the other way around. Once you plead guilty, it's usually for keeps.
Just say that you did substantial editing of the post while I was composing my answer. Let me add a quick thing.
Your research is correct. The examiner could find that this looks like an inadvertent mistake.
If however, he feels that it could be fraud -- second choice -- then he will turn the file over to the DA even if you do pay back the government. That's because this kind of fraud can be addressed legally in civil and/or criminal venues. Civilly, the government is looking specifically for its damages. Criminally, you can also be punished for the act. Payment doesn't prevent that.
If I've left anything out, use the reply box to send me a note and i'll be happy to address it.