After responding as available to a signing notification, it is then up to the company that sent out the notification to select the signing agent they'd like to work with. Learn more about how a signing starts and ends through Snapdocs.
While it may help to respond quickly to a notification, speed is not the only factor that determines whether you'll be assigned to the signing. Instead, each company has its own preferences or criteria when deciding who they would like to assign to a signing. In general though, many companies often consider a notary's bio, credentials, and work history.
Increasing your notary ranking may also help you get selected by the hiring company, since highly ranked signing agents will be some of the first to be notified of the signing opportunity. Being able to put in a response before other signing agents can help, but again, the speed of your response is not the only thing that determines whether you'll receive the signing opportunity.
If you are assigned to a signing, you will receive a confirmation via text and email to let you know. If you do not receive a confirmation to let you know you've been assigned, this likely means that the company assigned another signing agent. You can also see whether you've been assigned by checking your notification history.