While your small center is not required by your federal funder to conduct an annual audit, typically you are by other funding sources (check your contracts) and it is best practice for all.
The only federally required audit kicks in when you spend at least $750,000 in federal funds in a year. Then you are required to have the more expensive single audit of all federal funds which includes allowable and non-allowable costs.
Most centers have an independent firm conduct what is called a financial statement audit, which assures your funders that your financial statements are an accurate portrayal of your finances. This is what I recommend for you, but typically the auditor is secured by the board and they may want something more detailed when the Executive Director or Finance Director are replaced. You can collect a few bids, then give to the board for their decision. Then the auditor should report any findings directly to the board when the audit is complete.
The audit should occur as soon as possible after the close of your fiscal year. The auditor will also typically file your IRS Form 990 on your behalf. You should have done it annually, and it is required for you to keep your 501(c)3 status with the IRS. If you lose that status you lose eligibility to receive Title VII funds.