Hi RA,
It's not possible since you had given your answer on your question.
That IT0000 there have not PSA so PERNR will not be populated based on the PA,EG and ESG.
If you want to do this based on the PSA then user will assign manually when they knows employee will be hired on this PSA.
So my proposal is that you can design your PA accordingly PSA which will solve your query now and also check next stages combination.
Regards,
Sankarsan