Is it possible to determine its genotype by the phenotype of an organism?

This can be done, but not always.

Firstly, dominant traits are manifested in heterozygotes, therefore, it is impossible to accurately determine whether a person is hetero- or homozygous for this trait without analyzing the pedigree, but this does not give a guarantee.

Secondly, many signs do not appear externally or their manifestation depends on environmental conditions (for example, some diseases).

Thirdly, only genotypes based on recessive traits can be established with certainty. they appear in a homozygous state.