What do you mean.... " get the supervision "
are you being paid to do your line training? do you have a limited contract? or is it only type rating and base check?
Is the offer through or linked to an airline or is purely just a type rating training provider?
If you do get the NG rating with some line experience consider it very seriously, with the NG rating it's easy to fly any 737 from 300 series upwards.
Good luck
