When a bank originates an ACH (from a consumer account an another institution) to deposit funds into a consumer account (held by the bank), how soon must the funds be available?

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at open of business on the settlement date. Open of business per the NACHA rules is the later of 9:00 AM (RDFIs local time) or when the RDFIs teller facilities (including ATMs) are available for customer withdrawals.

Page OR23 of the NACHA rules is where you will find this

Hap, I believe you are thinking of ACH Credits.

If I am reading this correctly, the originating bank is actually originating a debit, those funds availability you listed do not apply. As a general rule, most banks will place a 2 day hold on the funds to allow for the possibility an NSF return.

The online bank I bank with places a 5 day on all deposits.

LCO83 is right. The credit to their own depositor isn't an ACH entry. It's an internal credit to which Reg CC doesn't apply. I deal with an online bank that gives me available credit two banking days after the Settlement Date for the ACH debit they send to my account at the other bank.