No. If you choose to make paycheck contributions to the HSA account, your annual election will be divided by the number of paychecks in the year. The amount will be deposited into your account each pay period, and only the amount that’s been deposited to date is available. You may not “borrow” against contributions not yet deposited in your account.
For this reason, if you expect to have significant health care costs immediately, you’ll want to be sure you budget adequately to pay for them out-of-pocket. You can be reimbursed from your HSA as your contributions are added to your account.