Can I start working for new company without H1B transfer?


I am currently working in a company A and project with that company is going to end soon and I have to leave the company. I have another job offer from company B(No specific joining date). Currently, my H1B is picked and I waiting for Approval. Once I receive an H1B approval can I start working for the new employer immediately without an H1B transfer? (which means applying for H1B transfer after October 1st while working for company B).