Is it permissible to use operating system files and programs provided by a training center, if their purchase is not confirmed, and this is for the sole purpose of training and without using them commercially or in practical life?

There is no harm in benefiting from the programs as long as you do not know that the entity has seized them, for the original state is that their ownership remains with them, and the original state for accidental attributes — such as usurpation and theft — is non-existence. If there is any sin, it is upon the entity that gave you authority over them.