A well-made concrete structure should not develop structural cracks quickly. However, fine cracks can be expected. Don't stress; these cracks aren't a sign of poor quality and can be fixed without much effort. Fine cracks in concrete should be repaired to prevent them from getting worse.
Yes, in about a month, fine cracks should disappear. While shrinkage cracks can appear on the surface within hours of pouring concrete, it takes a full month for new concrete to fully settle. Concrete surfaces cannot be repaired with concrete. Use a concrete repair mix instead; these are available at home centers and online.
Options include epoxy compounds, latex patch material, and mortar mixes. The latter option works best for filling large cracks (or chipped edges), while the other products are suitable for concrete cracks -inch wide or narrower. Common topical sealants can be used for concrete countertops, but getting them to penetrate and fill a fine crack can be difficult. Most concrete countertop sealants have a low solids content.
But using a material with a high solids content will ensure that, as the sealant cures, the material left in the crack will not shrink or separate from the concrete or, just as bad, leave a vacuum. A highly fluid epoxy (such as a fluid grade granite epoxy) will fill and seal a crack very well if it can get it into the crack. Keep in mind that materials such as epoxy are effective because they wet concrete. Functionally, this helps attract epoxy to the crack.
Aesthetically, this can cause the crack to have a darker appearance, especially if the sealant used in the countertop does not darken the concrete as much as epoxy does. ACI 116R-90, Cement and Concrete Terminology, defines fine cracks as cracks in an exposed concrete surface that have widths so small that they can barely be perceived. If your concrete is a little older, a concrete repair professional can help you fix the cracks. The causes of these cracks can be due to variations in air temperature, concrete temperature, relative humidity, and wind speed on the concrete surface.
After the concrete has fully cured, you can also consider using a concrete sealing compound to improve appearance and reduce cracking. If cracks appear right after pouring a concrete base, the concrete may have dried too quickly, mixed poorly, or overworked. The main cause behind the generation of fine cracks in concrete is plastic shrinkage, which is the rapid depletion of moisture from fresh concrete within its plastic state.