In the grace period of 60 days, can I still file in April for H1?

My OPT will start by February 2016. If I do no find a job that sponsors by April 2016, I will not be able to apply for H1-b and will have to work on my OPT, which would then expire by Feb 2017. If I am able to find one H1-b sponsoring company, how would the application work? In the grace-period of 60 days, can I still file in April for H1? Also, wanted to know till the time I get to know the results ie in the month of October, on what status can I stay here in USA?

An employer can still file for H-1 during the 60 day grace period. If you are selected in lottery, you will be eligible for cap-gap which allows you to stay inside US until Oct 1 or H-1 denial date (which ever is earlier).

However, you cannot work during this cap-gap period as your OPT would have expired and you were on grace period. You should keep your DSO in loop about this.

Thank you Saurabh. The information is useful and doubt is cleared. It is just hard for me to find an Accounting firm or company that sponsors entry level.