H1-B picked in second lottery, how to transfer it to new company before filing petition?

Hello Everyone,

I am currently on OPT and my H1-B got picked recently in second run of lottery. However the current company is still waiting to put me in a project as a contractor to file H1.

Also, I got a full time offer from a big firm recently.

Can the new company now file a petition for me by applying a transfer of my existing application, filed by previous company, which got selected?

I heard it can be done using form I 129 but USCIS mostly rejects is what I heard. Considering the current situations are there better chances USCIS might approve the transfer? Because if the current company is not in a position to file for me and the new company can. Will USCIS consider this?

Thank you and appreciate your time.