Govt Code 411.081d deals with non-disclosure (sealing) of criminal records. The part to which you refer states, "After notice to the state and a hearing on whether the person is entitled to file the petition and issuance of the order is in the best interest of justice, the court shall issue an order prohibiting criminal justice agencies from disclosing to the public criminal history record information related to the offense giving rise to the deferred adjudication."
The burden is to show that it is in the best interest of justice. You can be creative and argue that the only way you can get a good job is if the records are non-disclosed (sealed). Without being able to get the records sealed, the whole point of being allowed to plea to a deferred adjudication and your successful completion of it would all be for naught, i.e. you may not have received a conviction but employers (and the public) can still go on-line and see that you pled guilty to a criminal offense.
Please make an appointment and consult with a good criminal defense lawyer in your area.
Here's why. Texas has no statute for "sealing" criminal records. However, that is what you apparently think you are trying to do. You are asking how to convince the judge to do something Texas law does not provide for.
Put another way, you appear to be lost in the legal woods.
A first visit with a criminal lawyer is almost always at no cost. So, see a criminal defense lawyer and get things sorted out correctly.
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Mr. Sullivan assumes you filed a motion for an Order of Non-disclosure, and I will also. Furthermore, his idea for arguing how "sealing" your record is in the public interest is excellent. Another point in your favor is the prosecutor is unopposed to your motion. That means they probably recognize you are otherwise eligible for the non-dislosure order. However, they require you show "in the public interest" for their own CYA. I also agree that consulting with a qualified lawyer may also be in your best interest. Good luck.