Do I have to disclose that I've had a previous job?

Lying on a job application is cause for dismissal. Just say you had a job when and where. If asked just say you left because of differences with your former employer. Unless you stole or committed a crime is most likely does not matter. Lying on the other hand will always come back to bite you.

if your prospective employer discovers that detail after you've been hired, you are subject to immediate firing for cause [no unemployment] because you lied on the application. They'd then wonder, rightly, what other lies you may have told.

I had jobs that I don't list on my application, so it's perfectly acceptable

If you lie on an application. You should be honest.