Once the US government approves and grants the foreigner the H1B status, they can go on and get their visa and enter the US in September, and get themselves ready to start the job in October.
There are some employers that get exempted from the quota: government, academic institution, some NGO/non-profits. My path is through the exempted employers, but they would still need to pay the fees and get LCA and yadda yadda. Also, this path doesn't limit to the October intake (6/12)