TurboTax does not have your work history. The W-2's you entered into the tax software were only for the specific tax years in which you received income. W-2's do not not break down the income by the months in which you were paid. If you have had multiple employers then it is your responsibility to keep track of them and keep track of your dates of employment so that you can enter that information on job applications, resumes, unemployment compensation forms, etc. etc. etc. If you remember who the employers were you can contact them and ask them for the dates when you worked there.
Social Security keeps a work history but it might be completely up to date.
WORK HISTORY https://www.ssa.gov/forms/ssa-7050.pdf