Generally, the answer would be "no." Federal and State laws, generally, prohibit the sale or distribution of food to the general public without a license. Exceptions for low risk distribution (e.g. prepackaged food products) may be granted. Also, a child operating an neighborhood lemonade stand or selling baked goods would not be at risk, provided they were operating independently and not under the direction of a larger organized entity; even then the child would not be liable, the larger entity would be the one to be prosecuted or penalized. Typically, small time operations, that are one-time events, such as a church bake sale or school athletic booster event, are not subject to enforcement actions, as the risk of adverse health consequence to the public is relatively insignificant and usually involve nonprofit entities.
With regards to your cook-at-home-delivery business, which I presume would be for profit, you might be able to operate "under the radar" without a license for a while, but as the business grew, the likelihood of getting caught would also grow. Your state health department would be a good place to start inquiring about how to acquire the proper state license.
On a semi-related side note, given the health risk and possible resulting liability of providing food products, it would be worth looking into incorporating your business to limit the risk to and exposure of your personal assets.