If you read your offer letter, your offer is pending on background check. Another word, unless you pass the background check, there is no offer. Since they are not done with the background check yet, you are not an employee. How can they start processing your H1B?
After correction:
If you read your offer letter, you will see your offer is pending on background check. Another word, In other words, unless you pass the (Good! You didn't forget the "the" this time.) background check, there is no offer. Since they are not done with the background check yet, you are not an employee. How can they start processing your H1B?