Unfortunately, under USCIS's current policy and practice, unless and until you work for the sponsoring H-1B employer in H-1B status (after October 1, 2020), ano

Unfortunately, under USCIS's current policy and practice, unless and until you work for the sponsoring H-1B employer in H-1B status (after October 1, 2020), another company can't file an H-1B petition for you without going through the lottery again. Now USCIS could relax this policy (and sometimes USCIS doesn't follow it's own policy).