I fly airlines but here is how it works in KZAK (Oakland) airspace.
Login about 20 minutes before the FIR if inbound or anytime after leaving 10,000ft climbing if outbound from US West Coast. Once logged on immediately send a position report. It doesnt matter what position, it is only to satisfy the ground station that it has "data authority". How you do that from your installation I don't know.
Don't send another position unless asked, you won't be in the Pacific. We do a SELCAL check with SanFrancisco pre flight or early in the flight and then just monitor. Entering Auckland, Nadi or Brisbane FIRs we don't even call, just monitor the HF by SELCAL.
So to reiterate on your KOAK-PHNL flight.
Leaving 10000 on climb log on to KZAK.
Once logged on send a position report (without being asked).
Get a SELCAL check from San Francisco who will also give you new frequencies to change to at 140W.
Now no further action required except for level change requests etc. If you don't climb the next interaction with CPDLC would probably be a message to contact HNL Center approaching the Oceanic boundary inbound.