Entanglement results when the system under consideration belongs to one quantum mechanical solution of the specific problem.
The inflationary period as introduced at the beginning of the Big Bang model is a quantum mechanical solution to the boundary problem of the very early universe. At those sizes and energy densities it is assumed that everything is described with a quantum mechanical model. Specific models, are used to check consistency with the cosmic background radiation and the density of galaxy clusters in the observable universe, more or less successfully.
The dominant quantum field theoretical model presently is the one with a scalar field :
According to inflation theory, the inflaton is a scalar field that is responsible for cosmic inflation in the very early universe. A quantized particle for this field is expected, similar to other quantum fields, called an inflaton. The field provides a mechanism by which a period of rapid expansion from 10−35 to 10−34 seconds after the initial expansion can be generated, forming the universe .
It is consistent with the observation. The aim is to explain the observations and this quantum mechanical model leads to inflation at the early universe, and the fields and particles it posits are by construction entangled.
It is possible that another quantum mechanical model might describe the homogeneity of the observations without leading to rapid inflation, but it would be by different fields and boundary assumptions; entanglement will exist in any quantum mechanical model.