I have direct knowledge here - i design HFC/DOCSIS networks.
As MarkL Said:
Once the OS is booted, the RF can take a while to come up. The modem might have to search a large frequency space for a DOCSIS downstream carrier, and once found, perform a process called "ranging" where the modem starts transmitting at low power during specific ranging opportunity slots, while incrementally increasing power until the headend can hear it. Once the headend hears it, exact timing and power levels are set in another set of exchanges, the modem is authenticated, and then finally configured with and IP address and other provisioning information.
The most likely *actual* cause of this delay is that the firmware loaded on the modem doesn't have a scan list that is matching with atleast one of the frequencies used by downstream signals from the CMTS. In this instance, the modem has no choice but to blind scan for downstream channels after it's checked it's ~30 default scan channels. Depending on how smart the modem is, there's a good chance it'll have to find one of the 16 - 96 channels used by your ISP, exactly. And that's assuming a single ISP cable network - some networks have multiple carriers, and in that instance if your modem finds NOT your ISP first, it'll go through, try to sync, then fail, and start again when it gets booted off (i've done this myself, with 3 x CMTS's on a single cable segment).
The ISP has a couple of options to speed up boot (typically to about 30 seconds once a valid config has been loaded on to the modem once). Firstly - they modify downstream channel list in the CMTS (if they're able to) to one of the defaults in the scan list (typically ~30 channels listed) in the default firmware. Alternatively, they can pre-load a firmware with one of their channels included in the list (normally the firmware is created by the manufacturer of the modem, not the ISP - though larger ISPs could have their own dev's generate the firmware for them).
It only takes the modem to lock on to one of the downstream frequencies, and unless the ISP has configured otherwise, the full frequency list is included within the transmission - after that the modem knows every downstream frequency and upstream frequency, and begins the rest of the process. Bonding typically takes about 5-10 seconds at most, and then you're up to full speed.
Once the modem goes through this process, it *should* save that info for its next boot, and only in the case of a factory reset will it have to go through the blind scan again. It'll only save that info once it gets accepted into the CMTS.
By ensuring we have one of our channels in the scan list, we managed to drop our first start-up time from anywhere between 5-15 minutes, down to about 30 seconds (not including the config download and subsequent reboot after the config was downloaded (which only happens in case of config changes)).