Dear Disha,
There is no fixed policy on conversion of trainee to the confirmed employee. It will vary one company to another. However, the question arises is that why would you like to bypass the probation? As far as law is concerned, there is nothing like a "Trainee". It can be designation at the most. As such social securities like PF/ESI become applicable to the trainee or probationer or confirmed employee right from the first day of the employment.
As far as increase in salary is concerned, again it depends on your company policy. On completion of the training period, what designation would you like to give to him/her? What is paid to the persons at par with this designation, you need to pay to this person also. However, please make sure that you pay minimum wages at least on confirmation.
It appears that you do not have proper policy on permanent employment. You need to devise the policy first. Ad hoc decisions are not good as this could create imbalance and in turn it could demotivate few employees.
Thanks,
Dinesh Divekar