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. Don't be surprised if the cracks that seemed visible at first are almost impossible to see after a month of settlement. Fine cracks are commonly observed in freshly laid concrete and their appearance is due to the phenomenon of plastic shrinkage.
As the name implies, these cracks are very small, about 0.003 inches (0.08 mm) wide, and can be very shallow. 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.
Concrete naturally cracks on its own, unless it is given a place to crack, such as a control joint or expansion joint. As the concrete cures, it heats up and expands. In summer, I saw the slab crack before I could walk on it. There are other reasons for cracking, but one explanation takes much longer; and from your description I think you are witnessing shrinkage cracking.
As the concrete cures, excess water evaporates and the volume of the concrete at the inlet is reduced. And don't compact the soil when they fill it up; these are examples of cases where sedimentation cracks are likely to occur. It would be helpful to force the grout into the crack as much as possible to ensure that it fills the voids. Some shrinkage cracks are normal, but cracks throughout the slab are a sign that the concrete does not meet standards, may be weaker and less durable than necessary.
For a narrow crack like this, you can use a self-leveling concrete crack filler to seal the crack before painting or finishing the surface. It is important to closely follow the manufacturer's instructions for attaching the membrane to both concrete and tile. When the seal is embedded, it separates the surface near the stamped joints and causes small cracks around the outer edges of the “stones”. It won't give you a perfect color match, but it will keep out water and dirt and help stabilize the crack.
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. Over time, these drying and wetting cycles will cause its structure to crack in the same way that steel breaks after bending back and forth repeatedly. They often use wire mesh as reinforcement, which keeps concrete pieces together but doesn't prevent cracking. Since most fine cracks do not affect the structural integrity of a countertop, sealing and concealing the crack are the primary objectives of a repair.
A key factor is whether these are new cracks that are increasing in size or stable cracks that have been there for years and are not likely to increase in length or width.