Can we ask for a start date later than October 1st for a new H-1B?
Technically yes, but practically not possible in the current scenario. The H1B Petition can be filed only six months ahead of start date, i.e., the earliest filing date can be April 1st for the start date of October 1st. As the H1B numbers get capped on the first day (or soon thereafter) of the filing period, you cannot practically apply with a start date later than October 1st.