Knowing that in cluster sampling the population is divided into clusters and a simple random sample is taken of them and then all the elements of the chosen clusters are sampled, are the clusters in the beginning made randomly?
To answer the question, you should understand why a cluster is formed in the first place. Cluster sampling decreases accuracy of a survey and complicates statistics significantly. It's done because it's often the most convenient way to sample a population.
Generally, the cheapest and most efficient sampling method is to choose a subpopulation that is easy to sample. You would over-sample those "easy" subpopulation and under-sample the "harder" subpopulation. For example, it might be easier to sample schools in New York than schools away from the city.
So to answer your question, clusters are defined by the objective of the survey, and is generally not randomly chosen.
The clusters are usually made out of convenience. Cluster sampling usually has less precision than simple random samples or stratified samples, but SRS can be impractical in some situations.
One example is sampling 5th grade school children in the country. A SRS would require gathering the names of all the 5th grade children. Depending on the problem, after selecting the sample, people would have to cross the country to gather data across many different schools.
If cluster sampling, schools containing 5th grade would initially be collected. Then a smaller set of schools would be selected and traveled to.
Finally, I'm unsure if you are aware, but there is a two-stage sampling method which allows for a simple random sample of each selected school. What you describe in the question is a one-stage sampling method.