H1b lottery through. Question about Start date

Hi, my husband’s h1b lottery came through. We currently live in Taiwan so we will need to get stamping done in India before we go. The employer has not yet filed the LCA or petition - since they are a new company they took time to learn about the process. They will probably be ready to file next month. My question is - will his start date still be October 1st, regardless of when they file and when it gets approved? His was masters cap. Thanks!

Additionally, I would also like to know about premium processing of first time h1b. Can the employer do this? I read somewhere that they have to make an official announcement for premium processing which has not yet happened for this year. Please clarify…

Yes.

PP should be available as USCIS has not suspended PP this year as of now.