Travel during new H1B process

Hi ,
My H1B application picked in lottery in March 2021, I might be in a situation to travel India during my H1B petition in process( COS H4 to H1),
(1) If H1B petition gets approved while in India , can travel to US on H4 and apply COS from H4 to H1 after landing in US?
(2) If H1B petition gets approved while I am in USA itself ( before my travel date or Oct 2021 ) , can I travel to aUS on H4 and apply COS H4 to H1 after landing in US?
Appreciate your inputs. Thanks in advance.