The answer is anywhere from two business days to three weeks, and which one you get is mostly decided before you ask. The carrier's process has a fast path and a slow path, and the difference is paperwork you can do on a calm afternoon.
The fast path is electronic. If the carrier has your bank account on file for loan payouts, and you request the loan online or by phone, the money usually moves in a few business days. Some carriers process the request the same day and the transfer clears in two or three. Set that path up in your first ninety days, before you have any reason to use it. Log in, add the bank account, and verify it with the small test deposits if the carrier uses them.
The slow path is paper. If there's no bank account on file, the carrier mails a check, and between processing, printing, and the postal service you're looking at a week or two. Larger loan amounts often require a signed form rather than a phone request. And some carriers want a signature guarantee from your bank on big transfers, which means a trip to a branch. A few still require the owner's signature to be notarized above a certain amount. None of that is hard. All of it takes days if you find out about it after the water heater fails.
So here's the checklist for a calm afternoon. Make sure your bank account is on file and verified. Check that online access works. Save the loan request form where you can find it. And call the service line once to ask what dollar amount triggers the extra signature. Write the answer on the same page as the loan ledger. The steps of the request itself are in taking your first policy loan, step by step, and the setup work is in your first 90 days with a new policy. Interest starts accruing the day the loan is disbursed, and the death benefit and the available cash value are both smaller by the loan amount until you pay it back.
When the day comes, the loan request is a fifteen-minute job and the money is in checking before the plumber's invoice is due.