1. Technically, you can not do a transfer before you

are on H1 . However you can file a new H1.
2. You do not own the quota before you are on H1. So it is questionable if you are able to file a new H1.
3. CIS requires an applicant to work reasonable length of time for the sponshor before doing a transfer. So a picky officer may deny your transfer application if you have not worked for the first company for a reasonable length of time.