OP: new employers, especially if they're cap exempt, may not be able / willing to cover that fee. Thankfully you do not need a second approval for employment to begin, but if you have any international travel planned, then you should be ready to pay it if they are not willing.
H-1Bs are straightforward outside of the lottery, so if they're a cap exempt employer, and you need assistance, please reach out It's my day job!