Short answer; No.
Not without some hack I don't know of and wouldn't suggest, it is not possible to update the firmware via anything but coaxial. The log in credentials are user: [blank] Password: [blank]. The problem is certain information Cox (and other ISP's) considered proprietary was made viewable in the Cisco firmware so Cox stripped it down so it only shows what it does and is read only.
The log in system was specifically put in place by Cisco to give the providers a way to block certain content, but seeing how easy it is to Google such things, I understand why Cox chose not to use it. So basically its a room with a door with a lock that is unlocked, that leads directly into the exact same room. If you find out differently, please let me know, because my DPQ3212 has the same issue.
Your best bet is to contact Suddenlink. Does the modem sync up enough for them to see it? Even if it doesn't get online, if the modem gets a private IP in their system they may be able to push a new firmware to it. If it gets online and just isn't working well, chances are the new firmware will update itself. If it doesn't even sync up, you will probably have to buy a new modem.
And on that front, it looks like Suddenlink supports the DPC3010 but it doesn't "prefer" it. See link below. Thats why I like my modems like I like my underwear; not used. :3
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help.suddenlink.com/inte ··· ist.aspx