H1b Transfer Without Approval Notice (I-797a)

I am currently on OPT, which is going to expire at the end of Oct. I have check online and it shows my h1b has been approved 10 days ago, but I am still waiting for the approval notice. Meanwhile, I have received the approval notice for my wife (H4). H1b and H4 should start at the end of Oct as well (not Oct 1st, nonprofit organization). My question is whether it is possible to transfer H1b to another nonprofit organization without approval notice, but only the receipt number or receipt notice?

If you're not yet in status, no. You can't 'transfer' an H1B until you're in status.