Transfer H1b to new employer within a month of H1b approval without any payslip

[seeking_h1b]

Hi Everyone,

This is my situation. I had applied for H1b through a consultancy in April 2015 for consular processing from India. Since my husband was already in USA I came on H4 visa to USA in June 2015. My H1b petition was picked up in lottery but the approval didn't come till 23rd December. This approval came after we applied for premium processing + COS from H4 to H1. But the I-797 came without an attached I-94 (which was require since mine was a COS). So my employer wrote back to USCIS and then they sent me the corrected I-797 with the I-94 attached on 1st Feb 2016. Finally I applied for my SSN and the card came to me on 8th Feb 2016.

Because of these delays my employer doesnt have a project for me to start working on immediately. In the mean while I interviewed with a huge American MNC and they offered me a full time job. I really want to take it up since its with one of the biggies.

Is it possible for me to go ahead with asking them to file for my H1B transfer immediately? I have no payslip yet, will that cause a problem.

Anxiously waiting for a reply.