The modem scans for a digital channel with the correct DOCSIS packets in it. It then locks on that channel (first downstream channel) and starts decoding the data stream. Within that data stream is a Upstream Channel Description, which tells the modem which upstream channel to talk back to the cable headend equipment on.
Once the upstream and downstream are connected it gets further configuration information which includes any additional downstream and upstream channels, IP address, modem speed limits, allowed number of IPs, etc.
Once the connection is finished the cable headend equipment will perform periodic connection updates which can include instructions to change channels if the channels the modem is on are too busy or noisy.
Beyond the initial downstream channel search, the modem never chooses what channels to connect to, it's always told by the cable headend equipment what channels to connect to.--
If it's important, back it up... twice. Even 99.999% availability isn't enough sometimes.