No OPT? If you are on F-1, you can stay with pending H-1B(cap-gap clause),
but cannot work until Oct 1 if H-1B is approved.
Suppose employer files H-1B for you in April, 2018(BEFORE your graduation),
you can start working Oct 1, 2018 assuming 1)you are selected and 2)your
case is approved.
If employer files H-1B after you graduate, the earliest is April, 2019 since
H-1B will be gone after the first week of April, 2018, then you can start
working Oct 1, 2019 assuming 1)you are selected and 2)your case is approved,
but you need another legal status to stay here after your F-1 grade period
to Oct 1, 2019.Cap-Gap does not apply if you are not on F-1.
H-1B no cap is another way with more flexibility.