This sort of thing is common to most infections, it's simply not easy for a pathogen to effectively establish a symptomatic infection, you only have to consider how many pathogens we are exposed to, every day we even have large populations living on us and in us.
A virus firstly has to find a potential host, then overcome a variety of physical and chemical barriers, SARS-Cov-2 is a respiratory virus and infection usually requires infectious particles to enter the upper respiratory tract which is lined with mucus that acts as a trap as well as containing a variety of antiviral chemicals. The virus at this stage is not really considered to be alive and is essentially inert, it relies on chance and its large numbers to find a break in these defences. As it comes into contact with the cells lining the airways, it then needs to find a suitable point of entry to the cell and stick to it, this is normally the ACE2 receptor which is common in the respiratory tract, but it's still the case that not all cells will express this receptor. Apparently, the very young express few of these receptors, which is a possible explanation for the relative resistance of children under 1 to infection.
We have to consider that when we talk about the innate immune system we are not talking about a single mechanism, it provides layers of different defences, even as a virus gains entry to a cell it faces a number of hurdles to reach an appropriate place to be able to hijack the cells' machinery. As the virus takes over the cell is already signalling distress, this is a local effect that causes other cells to make entry of viruses more difficult. As the cell is increasingly damaged it increases its chemical signals, attracting a variety of specialist immune cells and as the virus particles are released this will result in the cell's death, a death that will be signalled. These responses are always graded and basically controlled by the strength of the chemical signalling, dealing with infection is metabolically very costly. All of this can be happening without any awareness, what happens is basically a competition between the viruses' ability to reproduce and find new target cells and the bodies escalating defences to stop them. One particular defence involves the immune cells conducting a cull of any local cells that are suspected of being infected, this cull becomes increasingly less selective and causes increasing chemical signalling. This is when we see the inflammatory and systemic responses to the infection, these are what cause the symptoms.
The adaptive immune responses are in fact activated quite early, T cells take an active role in killing infected cells even when the infection remains localised however the development of an effective antibody response requires the antigens to be present for some time. If the virus is eliminated quickly, it appears the process of antibody production is terminated. This virus has the ability to directly attack the immune cells, destroying the germinal centres that produce the B cells and reducing the overall population of other immune cells. Generally it is likely that the best antibody responses will be seen in people who develop symptomatic infections, and most people remain symptomatic for some time after viral clearance.
There will of course be all sorts of issues that might influence an individual's ability to quickly control the virus and of course features of the virus itself, we have seen the effects of a number of variants. This is all rather typical of how viral infections work, though Covid did add a few twists.
