Yes. There are sites on the internet which may show this information. You should hire an attorney to expunge your record pursuant to California Penal Code § 1203.4. You may even be able to do it yourself if you go to the criminal law clerk's office in your county. You should also be aware that even when you get your conviction expunged, sites on the internet may still show you have the conviction on your record.
If an order for relief pursuant to 1203.4 is granted, you are able to lawfully state that you have not been convicted of the crime when asked on a job application from a private (non-law enforcement) employer. The exceptions, where disclosure is required, are set out in the statute:
“The order does not relieve him of the obligation to disclose the conviction in response to any direct question contained in any questionnaire or application for public office, for licensure by any state or local agency, or for contracting with the California State Lottery.”
This means that if applying for public office, seeking any license from the state (real estate, stock broker, doctor, lawyer, etc.) or contracting with the California State Lottery, the conviction must be disclosed (although it can be disclosed as an expunged conviction).
You should verify you do not have to make such a disclosure for a job at a pre-school.
Also, please be aware that we have no attorney-client privilege and that this should not be considered legal advice. You should hire an attorney to answer all of your questions.