Genetic variation really only has one ultimate source, and that source is mutation. DNA is mutated all the time from background radiation, chemicals, and just random wear and tear. If an egg or sperm cell, or one of the cells of a very early-stage embryo, receives one of these mutations, then it can be carried into a new person and expressed there. Unfortunately for our scenario a high percentage of such mutations have bad outcomes.
In a population, gene flow adds variability - in a family, this would be created by the fact that people don't marry their near relatives, so "new blood" is being introduced to a family line in every generation.
The other mechanism is crossing over, which does not create new gene variants, but does shuffle the existing ones in new combinations. This occurs during meiosis, when homologous chromosomes are side by side, and they swap a section. This breaks up patterns and groups of genes, and the new combinations that result from it adds variability even in a group where no new members are being introduced.